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Bourjaily JL, Kalyanapuram N, Patatoukos K, Plesser M, Zhang Y. Gauge-Invariant Double Copies via Recursion Relations. PHYSICAL REVIEW LETTERS 2023; 131:191601. [PMID: 38000413 DOI: 10.1103/physrevlett.131.191601] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 10/05/2023] [Indexed: 11/26/2023]
Abstract
We prove by construction that all tree-level amplitudes in pure (super)gravity can be expressed as termwise, gauge-invariant double copies of those of pure (super-)Yang-Mills obtained via on-shell recursion. These representations are far from unique: varying the recursive scheme leads to a wide variety of distinct but equally valid representations of gravitational amplitudes, all realized as double copies.
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Affiliation(s)
- Jacob L Bourjaily
- Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Nikhil Kalyanapuram
- Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Kokkimidis Patatoukos
- Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Michael Plesser
- Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Yaqi Zhang
- Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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2
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Leston M, Goya A, Pérez-Nadal G, Passaglia M, Giribet G. 3D Quantum Gravity Partition Function at Three Loops. PHYSICAL REVIEW LETTERS 2023; 131:181601. [PMID: 37977604 DOI: 10.1103/physrevlett.131.181601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Accepted: 10/16/2023] [Indexed: 11/19/2023]
Abstract
The partition function of three-dimensional quantum gravity has been argued to be one-loop exact. Here, we verify the vanishing of higher orders in perturbation theory by explicit computation in the second-order metric formulation at three loops. The number of one-particle irreducible Feynman diagrams involving both gravitons and ghosts turns out to be 17. Using dimensional regularization, we solve all the diagrams. At two loops, we find that all such diagrams vanish separately after regularization. At three loops, in contrast, a series of remarkable cancellations between different diagrams takes place, with nine diagrams beautifully conspiring to yield a vanishing result. Our techniques are suitable to be applied to higher loops as well as to similar computations in higher dimensions.
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Affiliation(s)
- Mauricio Leston
- Instituto de Astronomía y Física del Espacio IAFE-CONICET, Ciudad Universitaria, IAFE, 1428 Buenos Aires, Argentina
- Departamento de Física, Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina
| | - Andrés Goya
- Instituto de Astronomía y Física del Espacio IAFE-CONICET, Ciudad Universitaria, IAFE, 1428 Buenos Aires, Argentina
| | - Guillem Pérez-Nadal
- Departamento de Física, Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina
| | - Mario Passaglia
- Departamento de Física, Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina
| | - Gaston Giribet
- Department of Physics, New York University, 726 Broadway, New York, New York 10003, USA
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3
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Hoffman DD, Prakash C, Prentner R. Fusions of Consciousness. ENTROPY (BASEL, SWITZERLAND) 2023; 25:129. [PMID: 36673270 PMCID: PMC9858210 DOI: 10.3390/e25010129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Revised: 01/02/2023] [Accepted: 01/03/2023] [Indexed: 06/17/2023]
Abstract
What are conscious experiences? Can they combine to form new experiences? What are conscious subjects? Can they combine to form new subjects? Most attempts to answer these questions assume that spacetime, and some of its particles, are fundamental. However, physicists tell us that spacetime cannot be fundamental. Spacetime, they say, is doomed. We heed the physicists, and drop the assumption that spacetime is fundamental. We assume instead that subjects and experiences are entities beyond spacetime, not within spacetime. We make this precise in a mathematical theory of conscious agents, whose dynamics are described by Markov chains. We show how (1) agents combine into more complex agents, (2) agents fuse into simpler agents, and (3) qualia fuse to create new qualia. The possible dynamics of n agents form an n(n-1)-dimensional polytope with nn vertices-the Markov polytopeMn. The total fusions of n agents and qualia form an (n-1)-dimensional simplex-the fusion simplexFn. To project the Markovian dynamics of conscious agents onto scattering processes in spacetime, we define a new map from Markov chains to decorated permutations. Such permutations-along with helicities, or masses and spins-invariantly encode all physical information used to compute scattering amplitudes. We propose that spacetime and scattering processes are a data structure that codes for interactions of conscious agents: a particle in spacetime is a projection of the Markovian dynamics of a communicating class of conscious agents.
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Affiliation(s)
- Donald D. Hoffman
- Department of Cognitive Sciences, University of California, Irvine, CA 92697, USA
| | - Chetan Prakash
- Department of Mathematics, California State University, San Bernadino, CA 92407, USA
- Association for Mathematical Consciousness Science, D-80539 Munich, Germany
| | - Robert Prentner
- Association for Mathematical Consciousness Science, D-80539 Munich, Germany
- Munich Center for Mathematical Philosophy, LMU Munich, D-80539 Munich, Germany
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4
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Leading Singularities in Higher-Derivative Yang–Mills Theory and Quadratic Gravity. UNIVERSE 2022. [DOI: 10.3390/universe8060326] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
In this work, we explore general leading singularities of one-loop amplitudes in higher-derivative Yang–Mills and quadratic gravity. These theories are known to possess propagators which contain quadratic and quartic momentum dependence, which leads to the presence of an unstable ghostlike resonance. However, unitarity cuts are not to be taken through unstable particles and therefore unitarity is still satisfied. On the other hand, this could engender issues when calculating leading singularities which are generalizations of unitarity cuts. Nevertheless, we will show with explicit examples how leading singularities are still well defined and accordingly they are able to capture relevant information on the analytic structure of amplitudes in such higher-derivative theories. We discuss some simple one-loop amplitudes which clarify these features.
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Bepari K, Malik S, Spannowsky M, Williams S. Towards a quantum computing algorithm for helicity amplitudes and parton showers. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.103.076020] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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6
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Brown F, Dupont C. Single-Valued Integration and Superstring Amplitudes in Genus Zero. COMMUNICATIONS IN MATHEMATICAL PHYSICS 2021; 382:815-874. [PMID: 33758427 PMCID: PMC7940340 DOI: 10.1007/s00220-021-03969-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/05/2019] [Accepted: 01/15/2021] [Indexed: 06/12/2023]
Abstract
We study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper (Brown and Dupont in Single-valued integration and double copy, 2020). Using dihedral coordinates on the moduli spaces of curves of genus zero with marked points, we define a canonical regularisation of both open and closed string perturbation amplitudes at tree level, and deduce that they admit a Laurent expansion in Mandelstam variables whose coefficients are multiple zeta values (resp. single-valued multiple zeta values). Furthermore, we prove the existence of a motivic Laurent expansion whose image under the period map is the open string expansion, and whose image under the single-valued period map is the closed string expansion. This proves the recent conjecture of Stieberger that closed string amplitudes are the single-valued projections of (motivic lifts of) open string amplitudes. Finally, applying a variant of the single-valued formalism for cohomology with coefficients yields the KLT formula expressing closed string amplitudes as quadratic expressions in open string amplitudes.
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Affiliation(s)
| | - Clément Dupont
- Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, CNRS, Montpellier, France
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7
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Adamo T, Mason L, Sharma A. Maximal-Helicity-Violating Scattering of Gluons and Gravitons in Chiral Strong Fields. PHYSICAL REVIEW LETTERS 2020; 125:041602. [PMID: 32794784 DOI: 10.1103/physrevlett.125.041602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2020] [Accepted: 07/10/2020] [Indexed: 06/11/2023]
Abstract
We present all-multiplicity formulas for the tree-level scattering of gluons and gravitons in the maximal helicity violating (MHV) helicity configuration, calculated in certain chiral strong fields. The strong backgrounds we consider are self-dual plane waves in gauge theory and general relativity, which are treated exactly and admit a well-defined S matrix. The gauge theory background-coupled MHV amplitude is simply a dressed analog of the familiar Parke-Taylor formula, but the gravitational version has nontrivial new structures due to graviton tails. Both formulas have just one residual integral rather than the n-2 expected at n points from space-time perturbation theory; this simplification arises from the integrability of self-dual backgrounds and their corresponding twistor description. The resulting formulas pass several consistency checks and limit to the well-known expressions for MHV scattering of gluons and gravitons when the background becomes trivial.
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Affiliation(s)
- Tim Adamo
- School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Lionel Mason
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - Atul Sharma
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
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Bourjaily JL, Herrmann E, Langer C, McLeod AJ, Trnka J. All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops. PHYSICAL REVIEW LETTERS 2020; 124:111603. [PMID: 32242737 DOI: 10.1103/physrevlett.124.111603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2019] [Accepted: 02/28/2020] [Indexed: 06/11/2023]
Abstract
We give a prescriptive representation of all-multiplicity two-loop maximally-helicity-violating (MHV) amplitude integrands in fully-color-dressed (nonplanar) maximally supersymmetric Yang-Mills theory.
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Affiliation(s)
- Jacob L Bourjaily
- Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
- Center for the Fundamental Laws of Nature, Department of Physics, Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA
- Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16892, USA
| | - Enrico Herrmann
- SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94039, USA
| | - Cameron Langer
- Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, California 95616, USA
| | - Andrew J McLeod
- Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
| | - Jaroslav Trnka
- Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, California 95616, USA
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9
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Badger S, Chicherin D, Gehrmann T, Heinrich G, Henn JM, Peraro T, Wasser P, Zhang Y, Zoia S. Analytic Form of the Full Two-Loop Five-Gluon All-Plus Helicity Amplitude. PHYSICAL REVIEW LETTERS 2019; 123:071601. [PMID: 31491100 DOI: 10.1103/physrevlett.123.071601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2019] [Indexed: 06/10/2023]
Abstract
We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms, and rational functions.
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Affiliation(s)
- S Badger
- Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, United Kingdom
| | - D Chicherin
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
| | - T Gehrmann
- Physik-Institut, Universität Zürich, Wintherturerstrasse 190, CH-8057 Zürich, Switzerland
| | - G Heinrich
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
| | - J M Henn
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
| | - T Peraro
- Physik-Institut, Universität Zürich, Wintherturerstrasse 190, CH-8057 Zürich, Switzerland
| | - P Wasser
- PRISMA+Cluster of Excellence, Johannes Gutenberg University, D-55099 Mainz, Germany
| | - Y Zhang
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
- Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - S Zoia
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
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10
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Antonelli A, Buonanno A, Steinhoff J, van de Meent M, Vines J. Energetics of two-body Hamiltonians in post-Minkowskian gravity. Int J Clin Exp Med 2019. [DOI: 10.1103/physrevd.99.104004] [Citation(s) in RCA: 82] [Impact Index Per Article: 16.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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11
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Chicherin D, Gehrmann T, Henn JM, Wasser P, Zhang Y, Zoia S. Analytic Result for a Two-Loop Five-Particle Amplitude. PHYSICAL REVIEW LETTERS 2019; 122:121602. [PMID: 30978051 DOI: 10.1103/physrevlett.122.121602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2018] [Indexed: 06/09/2023]
Abstract
We compute the symbol of the full-color two-loop five-particle amplitude in N=4 super Yang-Mills theory, including all nonplanar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the nonplanar terms, analyze its subleading power corrections, and analytically present the leading logarithmic terms.
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Affiliation(s)
- D Chicherin
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
| | - T Gehrmann
- Physik-Institut, Universität Zürich, Wintherturerstrasse 190, CH-8057 Zürich, Switzerland
| | - J M Henn
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
| | - P Wasser
- PRISMA Cluster of Excellence, Johannes Gutenberg University, D-55099 Mainz, Germany
| | - Y Zhang
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
| | - S Zoia
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
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12
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Abreu S, Dixon LJ, Herrmann E, Page B, Zeng M. Two-Loop Five-Point Amplitude in N=4 Super-Yang-Mills Theory. PHYSICAL REVIEW LETTERS 2019; 122:121603. [PMID: 30978096 DOI: 10.1103/physrevlett.122.121603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2019] [Indexed: 06/09/2023]
Abstract
We compute the symbol of the two-loop five-point scattering amplitude in N=4 supersymmetric Yang-Mills theory, including its full color dependence. This requires constructing the symbol of all two-loop five-point nonplanar massless master integrals, for which we give explicit results.
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Affiliation(s)
- Samuel Abreu
- Center for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium
| | - Lance J Dixon
- SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94039, USA
| | - Enrico Herrmann
- SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94039, USA
| | - Ben Page
- Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay, F-91191 Gif-sur-Yvette cedex, France
| | - Mao Zeng
- Institut für Theoretische Physik, Eidgenössische Technische Hochschule Zürich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland
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13
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Bern Z, Enciso M, Shen CH, Zeng M. Dual Conformal Structure Beyond the Planar Limit. PHYSICAL REVIEW LETTERS 2018; 121:121603. [PMID: 30296163 DOI: 10.1103/physrevlett.121.121603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2018] [Indexed: 06/08/2023]
Abstract
The planar scattering amplitudes of N=4 super-Yang-Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at infinity. Recent work shows in various nontrivial examples that the simple analytic properties of the planar sector survive into the nonplanar sector, but this has yet to be understood from underlying symmetries. Here, we explicitly show that for an infinite class of nonplanar integrals that covers all subleading-color contributions to the two-loop four- and five-point amplitudes of N=4 super-Yang-Mills theory, symmetries analogous to dual conformal invariance exist. A natural conjecture is that this continues to all amplitudes of the theory at any loop order.
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Affiliation(s)
- Zvi Bern
- Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Michael Enciso
- Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Chia-Hsien Shen
- Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Mao Zeng
- Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095, USA
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14
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Atiyah M, Dunajski M, Mason LJ. Twistor theory at fifty: from contour integrals to twistor strings. Proc Math Phys Eng Sci 2017; 473:20170530. [PMID: 29118667 DOI: 10.1098/rspa.2017.0530] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2017] [Accepted: 09/08/2017] [Indexed: 11/12/2022] Open
Abstract
We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space-time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold-the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics-anti-self-duality equations on Yang-Mills or conformal curvature-can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang-Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang-Mills equations, and Einstein-Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose's proposal for a role of gravity in quantum collapse of a wave function.
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Affiliation(s)
- Michael Atiyah
- School of Mathematics, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, UK.,Trinity College Cambridge, University of Cambridge, Cambridge CB2 1TQ, UK
| | - Maciej Dunajski
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
| | - Lionel J Mason
- The Mathematical Institute, Andrew Wiles Building, University of Oxford, Oxford OX2 6GG, UK
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15
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Rastelli L, Zhou X. Mellin Amplitudes for Supergravity on AdS_{5}×S^{5}. PHYSICAL REVIEW LETTERS 2017; 118:091602. [PMID: 28306290 DOI: 10.1103/physrevlett.118.091602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2016] [Indexed: 06/06/2023]
Abstract
We revisit the calculation of holographic correlation functions in type-IIB supergravity on AdS_{5}×S^{5}. Results for four-point functions simplify drastically when expressed in Mellin space. We conjecture a compact formula for the four-point functions of one-half Bogomol'nyi-Prasad-Sommerfield single-trace operators of arbitrary weight. Our methods rely on general consistency conditions and eschew detailed knowledge of the supergravity effective action.
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Affiliation(s)
- Leonardo Rastelli
- C.N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794, USA
| | - Xinan Zhou
- C.N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794, USA
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16
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17
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18
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Hodges A. Twistors and amplitudes. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2015; 373:rsta.2014.0248. [PMID: 26124244 DOI: 10.1098/rsta.2014.0248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/27/2015] [Indexed: 06/04/2023]
Abstract
A brief review is given of why twistor geometry has taken a central place in the theory of scattering amplitudes for fundamental particles. The emphasis is on the twistor diagram formalism as originally proposed by Penrose, the development of which has now led to the definition by Arkani-Hamed et al. of the 'amplituhedron'.
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Affiliation(s)
- Andrew Hodges
- Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
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19
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20
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Brambilla N, Eidelman S, Foka P, Gardner S, Kronfeld AS, Alford MG, Alkofer R, Butenschoen M, Cohen TD, Erdmenger J, Fabbietti L, Faber M, Goity JL, Ketzer B, Lin HW, Llanes-Estrada FJ, Meyer HB, Pakhlov P, Pallante E, Polikarpov MI, Sazdjian H, Schmitt A, Snow WM, Vairo A, Vogt R, Vuorinen A, Wittig H, Arnold P, Christakoglou P, Di Nezza P, Fodor Z, Garcia i Tormo X, Höllwieser R, Janik MA, Kalweit A, Keane D, Kiritsis E, Mischke A, Mizuk R, Odyniec G, Papadodimas K, Pich A, Pittau R, Qiu JW, Ricciardi G, Salgado CA, Schwenzer K, Stefanis NG, von Hippel GM, Zakharov VI. QCD and strongly coupled gauge theories: challenges and perspectives. THE EUROPEAN PHYSICAL JOURNAL. C, PARTICLES AND FIELDS 2014; 74:2981. [PMID: 25972760 PMCID: PMC4413533 DOI: 10.1140/epjc/s10052-014-2981-5] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2014] [Accepted: 07/05/2014] [Indexed: 05/17/2023]
Abstract
We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.
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Affiliation(s)
- N. Brambilla
- Physik Department, Technische Universität München, James-Franck-Straße 1, 85748 Garching, Germany
| | - S. Eidelman
- Budker Institute of Nuclear Physics, SB RAS, Novosibirsk , 630090 Russia
- Novosibirsk State University, Novosibirsk , 630090 Russia
| | - P. Foka
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291 Darmstadt, Germany
| | - S. Gardner
- Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506-0055 USA
| | - A. S. Kronfeld
- Theoretical Physics Department, Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510-5011 USA
| | - M. G. Alford
- Department of Physics, Washington University, St Louis, MO 63130 USA
| | | | - M. Butenschoen
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Wien, Austria
| | - T. D. Cohen
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, MD 20742-4111 USA
| | - J. Erdmenger
- Max-Planck-Institute for Physics, Föhringer Ring 6, 80805 Munich, Germany
| | - L. Fabbietti
- Excellence Cluster “Origin and Structure of the Universe”, Technische Universität München, 85748 Garching, Germany
| | - M. Faber
- Atominstitut, Technische Universität Wien, 1040 Vienna, Austria
| | - J. L. Goity
- Hampton University, Hampton, VA 23668 USA
- Jefferson Laboratory, Newport News, VA 23606 USA
| | - B. Ketzer
- Physik Department, Technische Universität München, James-Franck-Straße 1, 85748 Garching, Germany
- Present Address: Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn, 53115 Bonn, Germany
| | - H. W. Lin
- Department of Physics, University of Washington, Seattle, WA 98195-1560 USA
| | - F. J. Llanes-Estrada
- Department Fisica Teorica I, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - H. B. Meyer
- PRISMA Cluster of Excellence, Institut für Kernphysik and Helmholtz Institut Mainz, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
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- Institute of Theoretical and Experimental Physics, Moscow, 117218 Russia
- Moscow Institute for Physics and Technology, Dolgoprudny, 141700 Russia
| | - E. Pallante
- Centre for Theoretical Physics, University of Groningen, 9747 AG Groningen, The Netherlands
| | - M. I. Polikarpov
- Institute of Theoretical and Experimental Physics, Moscow, 117218 Russia
- Moscow Institute for Physics and Technology, Dolgoprudny, 141700 Russia
| | - H. Sazdjian
- Institut de Physique Nucléaire CNRS/IN2P3, Université Paris-Sud, 91405 Orsay, France
| | - A. Schmitt
- Institut für Theoretische Physik, Technische Universität Wien, 1040 Vienna, Austria
| | - W. M. Snow
- Center for Exploration of Energy and Matter and Department of Physics, Indiana University, Bloomington, IN 47408 USA
| | - A. Vairo
- Physik Department, Technische Universität München, James-Franck-Straße 1, 85748 Garching, Germany
| | - R. Vogt
- Physics Division, Lawrence Livermore National Laboratory, Livermore, CA 94551 USA
- Physics Department, University of California, Davis, CA 95616 USA
| | - A. Vuorinen
- Department of Physics and Helsinki Institute of Physics, University of Helsinki, Helsinki, P.O. Box 64, 00014 Finland
| | - H. Wittig
- PRISMA Cluster of Excellence, Institut für Kernphysik and Helmholtz Institut Mainz, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
| | - P. Arnold
- Department of Physics, University of Virginia, 382 McCormick Rd., P.O. Box 400714, Charlottesville, VA 22904-4714 USA
| | | | - P. Di Nezza
- Istituto Nazionale di Fisica Nucleare (INFN), Via E. Fermi 40, 00044 Frascati, Italy
| | - Z. Fodor
- Wuppertal University, 42119 Wuppertal, Germany
- Eötvös University, 1117 Budapest, Hungary
- Forschungszentrum Jülich, 52425 Jülich, Germany
| | - X. Garcia i Tormo
- Albert Einstein Center for Fundamental Physics, Institut für Theoretische Physik, Universität Bern, Sidlerstraße 5, 3012 Bern, Switzerland
| | - R. Höllwieser
- Atominstitut, Technische Universität Wien, 1040 Vienna, Austria
| | - M. A. Janik
- Faculty of Physics, Warsaw University of Technology, 00-662 Warsaw, Poland
| | - A. Kalweit
- European Organization for Nuclear Research (CERN), Geneva, Switzerland
| | - D. Keane
- Department of Physics, Kent State University, Kent, OH 44242 USA
| | - E. Kiritsis
- Crete Center for Theoretical Physics, Department of Physics, University of Crete, 71003 Heraklion, Greece
- Laboratoire APC, Université Paris Diderot, Paris Cedex 13, Sorbonne Paris-Cité , 75205 France
- Theory Group, Physics Department, CERN, 1211 Geneva 23, Switzerland
| | - A. Mischke
- Faculty of Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - R. Mizuk
- Institute of Theoretical and Experimental Physics, Moscow, 117218 Russia
- Moscow Physical Engineering Institute, Moscow, 115409 Russia
| | - G. Odyniec
- Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, CA 94720 USA
| | - K. Papadodimas
- Centre for Theoretical Physics, University of Groningen, 9747 AG Groningen, The Netherlands
| | - A. Pich
- IFIC, Universitat de València, CSIC, Apt. Correus 22085, 46071 València, Spain
| | - R. Pittau
- Departamento de Fisica Teorica y del Cosmos and CAFPE, Campus Fuentenueva s. n., Universidad de Granada, 18071 Granada, Spain
| | - J.-W. Qiu
- Physics Department, Brookhaven National Laboratory, Upton, NY 11973 USA
- C. N. Yang Institute for Theoretical Physics and Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794 USA
| | - G. Ricciardi
- Dipartimento di Fisica, Università degli Studi di Napoli Federico II, 80126 Napoli, Italy
- INFN, Sezione di Napoli, 80126 Napoli, Italy
| | - C. A. Salgado
- Departamento de Fisica de Particulas y IGFAE, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Galicia, Spain
| | - K. Schwenzer
- Department of Physics, Washington University, St Louis, MO 63130 USA
| | - N. G. Stefanis
- Institut für Theoretische Physik II, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - G. M. von Hippel
- PRISMA Cluster of Excellence, Institut für Kernphysik and Helmholtz Institut Mainz, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
| | - V. I. Zakharov
- Max-Planck-Institute for Physics, Föhringer Ring 6, 80805 Munich, Germany
- Institute of Theoretical and Experimental Physics, Moscow, 117218 Russia
- Moscow Institute for Physics and Technology, Dolgoprudny, 141700 Russia
- School of Biomedicine, Far Eastern Federal University, Sukhanova str 8, Vladivostok, 690950 Russia
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Badger S, Biedermann B, Hackl L, Plefka J, Schuster T, Uwer P. Comparing efficient computation methods for massless QCD tree amplitudes: Closed analytic formulas versus Berends-Giele recursion. Int J Clin Exp Med 2013. [DOI: 10.1103/physrevd.87.034011] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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23
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Adamo T, Mason L. Maximally helicity-violating diagrams in twistor space and the twistor action. Int J Clin Exp Med 2012. [DOI: 10.1103/physrevd.86.065019] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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24
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Boels RH. Maximal R-symmetry violating amplitudes in type IIb superstring theory. PHYSICAL REVIEW LETTERS 2012; 109:081602. [PMID: 23002738 DOI: 10.1103/physrevlett.109.081602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2012] [Indexed: 06/01/2023]
Abstract
On-shell superspace techniques are used to quantify R-symmetry violation in type IIB superstring theory amplitudes in a flat background in 10 dimensions. This shows the existence of a particularly simple class of nonvanishing amplitudes in this theory, which violate R symmetry maximally. General properties of the class and some of its extensions are established that at string tree level are shown to determine the first three nontrivial effective field theory contributions to all multiplicity. This leads to a natural conjecture for the exact analytic part of the first two of these.
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Affiliation(s)
- Rutger H Boels
- II. Institut für Theoretische Physik, Universität Hamburg, Hamburg, Germany.
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Dunbar DC, Ettle JH, Perkins WB. Maximal-helicity-violating n-point one-loop amplitude in N=4 supergravity. PHYSICAL REVIEW LETTERS 2012; 108:061603. [PMID: 22401057 DOI: 10.1103/physrevlett.108.061603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2011] [Indexed: 05/31/2023]
Abstract
We propose an explicit formula for the n-point maximal-helicity-violating one-loop amplitude in a N=4 supergravity theory. This formula is derived from the soft and collinear factorizations of the amplitude.
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Affiliation(s)
- David C Dunbar
- College of Science, Swansea University, Swansea, United Kingdom
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Angioni M, Chachamis G, Madrigal JD, Sabio Vera A. Dijet production at large rapidity separation in N = 4 supersymmetric Yang-Mills theory. PHYSICAL REVIEW LETTERS 2011; 107:191601. [PMID: 22181595 DOI: 10.1103/physrevlett.107.191601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2011] [Indexed: 05/31/2023]
Abstract
Ratios of azimuthal angle correlations between two jets produced at large rapidity separation are studied in the N = 4 maximally supersymmetric Yang-Mills (MSYM) theory. It is shown that these observables, which directly prove the SL(2,C) symmetry present in gauge theories in the Regge limit, exhibit an excellent perturbative convergence. They are compared to those calculated in QCD for different renormalization schemes concluding that the momentum-substraction scheme with the Brodsky-Lepage-Mackenzie scale-fixing procedure captures the bulk of the MSYM results.
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Affiliation(s)
- M Angioni
- Dipartimento di Fisica, Università di Firenze, Italy
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Beisert N, Schwab BUW. Bonus Yangian symmetry for the planar S matrix of N=4 supersymmetric Yang-Mills theory. PHYSICAL REVIEW LETTERS 2011; 106:231602. [PMID: 21770496 DOI: 10.1103/physrevlett.106.231602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2011] [Indexed: 05/31/2023]
Abstract
Recent developments in the determination of the planar S matrix of N=4 super Yang-Mills are closely related to its Yangian symmetry. Here we provide evidence for a yet unobserved additional symmetry: the Yangian level-one helicity operator.
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Affiliation(s)
- Niklas Beisert
- Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Potsdam, Germany.
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28
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Chen G. Recursion relations for the general tree-level amplitudes in QCD with massive Dirac fields. Int J Clin Exp Med 2011. [DOI: 10.1103/physrevd.83.125005] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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29
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Stieberger S. Constraints on tree-level higher order gravitational couplings in superstring theory. PHYSICAL REVIEW LETTERS 2011; 106:111601. [PMID: 21469856 DOI: 10.1103/physrevlett.106.111601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/01/2011] [Indexed: 05/30/2023]
Abstract
We consider the scattering amplitudes of five and six gravitons at tree level in superstring theory. Their power series expansions in the Regge slope α' are analyzed through the order α'(8) showing some interesting constraints on higher order gravitational couplings in the effective superstring action such as the absence of R(5) terms. Furthermore, some transcendentality constraints on the coefficients of the nonvanishing couplings are observed: the absence of zeta values of even weight through the order α'(8) like the absence of ζ(2)ζ(3)R(6) terms. Our analysis is valid for any superstring background in any space-time dimension, which allows for a conformal field theory description.
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Affiliation(s)
- Stephan Stieberger
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München, Germany
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30
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Turok N. Beyond Feynman's diagrams. Nature 2011; 469:165-6. [DOI: 10.1038/469165a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Bork LV, Kazakov DI, Vartanov GS, Zhiboedov AV. Construction of infrared finite observables inN=4super Yang-Mills theory. Int J Clin Exp Med 2010. [DOI: 10.1103/physrevd.81.105028] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Anchordoqui LA, Goldberg H, Nawata S, Taylor TR. Jet signals for low mass strings at the large hadron collider. PHYSICAL REVIEW LETTERS 2008; 100:171603. [PMID: 18518273 DOI: 10.1103/physrevlett.100.171603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2007] [Revised: 03/02/2008] [Indexed: 05/26/2023]
Abstract
The mass scale M{s} of superstring theory is an arbitrary parameter that can be as low as few TeVs if the Universe contains large extra dimensions. We propose a search for the effects of Regge excitations of fundamental strings at the CERN Large Hadron Collider (LHC), in the process pp-->gamma+jet. The underlying parton process is dominantly the single photon production in gluon fusion, gg-->gammag, with open string states propagating in intermediate channels. If the photon mixes with the gauge boson of the baryon number, which is a common feature of D-brane quivers, the amplitude appears already at the string disk level. It is completely determined by the mixing parameter-and it is otherwise model (compactification) independent. Even for relatively small mixing, 100 fb{-1} of LHC data could probe deviations from standard model physics, at a 5sigma significance, for M{s} as large as 3.3 TeV.
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Affiliation(s)
- Luis A Anchordoqui
- Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA
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Boels R. A quantization of twistor Yang-Mills theory through the background field method. Int J Clin Exp Med 2007. [DOI: 10.1103/physrevd.76.105027] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Stieberger S, Taylor TR. Amplitude for N-gluon superstring scattering. PHYSICAL REVIEW LETTERS 2006; 97:211601. [PMID: 17155734 DOI: 10.1103/physrevlett.97.211601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2006] [Indexed: 05/12/2023]
Abstract
We consider scattering processes involving N gluonic massless states of open superstrings with a certain Regge slope alpha'. At the semiclassical level, the string world-sheet sweeps a disk and N gluons are created or annihilated at the boundary. We present exact expressions for the corresponding amplitudes, valid to all orders in alpha', for the so-called maximally helicity violating configurations, with N = 4, 5 and N = 6. We also obtain the leading O(alpha '2) string corrections to the zero-slope N-gluon Yang-Mills amplitudes.
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Affiliation(s)
- Stephan Stieberger
- Arnold-Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany
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Draggiotis P, van Hameren A, Kleiss R, Lazopoulos A, Papadopoulos C, Worek M. Recursive equations for arbitrary scattering processes. ACTA ACUST UNITED AC 2006. [DOI: 10.1016/j.nuclphysbps.2006.09.053] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Ferrario P, Rodrigo G, Talavera P. Compact multigluonic scattering amplitudes with heavy scalars and fermions. PHYSICAL REVIEW LETTERS 2006; 96:182001. [PMID: 16712359 DOI: 10.1103/physrevlett.96.182001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2006] [Indexed: 05/09/2023]
Abstract
Combining the Berends-Giele and on-shell recursion relations we obtain an extremely compact expression for the scattering amplitude of a complex massive scalar-antiscalar pair and an arbitrary number of positive helicity gluons. This is one of the basic building blocks for constructing other helicity configurations from recursion relations. We also show explicitly that the scattering amplitude of massive fermions to gluons, all with positive helicity, is proportional to the scalar one, confirming in this way the recently advocated SUSY-like Ward identities relating both amplitudes.
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Affiliation(s)
- Paola Ferrario
- Instituto de Física Corpuscular, CSIC-Universitat de València, Apartado de Correos 22085, E-46071 Valencia, Spain.
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Chiou DW, Ganor OJ, Hong YP, Kim BS, Mitra I. Massless and massive three-dimensional super Yang-Mills theory and mini-twistor string theory. Int J Clin Exp Med 2005. [DOI: 10.1103/physrevd.71.125016] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Roiban R, Volovich A. All conjugate-maximal-helicity-violating amplitudes from topological open string theory in twistor space. PHYSICAL REVIEW LETTERS 2004; 93:131602. [PMID: 15524702 DOI: 10.1103/physrevlett.93.131602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2004] [Indexed: 05/24/2023]
Abstract
It has recently been proposed that the D-instanton expansion of the open topological B model on P(3|4) is equivalent to the perturbative expansion of the maximally supersymmetric Yang-Mills theory in four dimensions. In this letter we show how to construct the gauge theory results for all n-point conjugate-maximal-helicity-violating amplitudes by computing the integral over the moduli space of curves of degree n-3 in P(3|4), providing strong support to the string theory construction.
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Affiliation(s)
- Radu Roiban
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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Bern Z. Perturbative Quantum Gravity and its Relation to Gauge Theory. LIVING REVIEWS IN RELATIVITY 2002; 5:5. [PMID: 28163636 PMCID: PMC5255540 DOI: 10.12942/lrr-2002-5] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on D-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input the gravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.
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Affiliation(s)
- Zvi Bern
- Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, CA 90095 USA
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Bern Z, De Freitas A, Wong HL. Coupling gravitons to matter. PHYSICAL REVIEW LETTERS 2000; 84:3531-3534. [PMID: 11019138 DOI: 10.1103/physrevlett.84.3531] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/1999] [Indexed: 05/23/2023]
Abstract
Using relationships between open and closed strings, we present a construction of tree-level scattering amplitudes for gravitons minimally coupled to matter in terms of gauge theory partial amplitudes. In particular, we present examples of amplitudes with gravitons coupled to vectors or to a single fermion pair. We also present two examples with massive graviton exchange, as would arise in the presence of large compact dimensions. The gauge charges are represented by flavors of dynamical scalars or fermions. This also leads to an unconventional decomposition of color and kinematics in gauge theories.
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Affiliation(s)
- Z Bern
- Department of Physics and Astronomy, The University of California at Los Angeles, Los Angeles, California 90095-1547, USA
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Chalmers G, Siegel W. Self-dual sector of QCD amplitudes. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1996; 54:7628-7633. [PMID: 10020775 DOI: 10.1103/physrevd.54.7628] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Del Duca V. Quark-antiquark contribution to the multigluon amplitudes in the helicity formalism. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1996; 54:4474-4482. [PMID: 10021130 DOI: 10.1103/physrevd.54.4474] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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50
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Del Duca V. Real next-to-leading corrections to the multigluon amplitudes in the helicity formalism. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1996; 54:989-1009. [PMID: 10020564 DOI: 10.1103/physrevd.54.989] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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