New Diagrammatic Framework for Higher-Spin Gravity

We consider minimal type-A higher-spin (HS) gravity in four dimensions, at tree level. We propose new diagrammatic rules for this theory, involving both Fronsdal fields and Didenko-Vasiliev particles-linearized versions of HS gravity's "BPS black hole." The vertices include a standard minimal coupling between particle and gauge field, the Sleight-Taronna cubic vertex for HS fields, and a recently introduced vertex coupling two HS fields to a Didenko-Vasiliev particle. We show how these ingredients can be combined to reproduce all n-point functions of the theory's holographic dual-the free O(N) vector model. Our diagrammatic rules interpolate between the usual diagrammatic rules of field theory and those of string theory. Our construction can be viewed as a bulk realization of HS algebra.

Chiral Approach to Massive Higher Spins

We propose a new, chiral description for massive higher-spin particles in four spacetime dimensions, which facilitates the introduction of consistent interactions. As proof of concept, we formulate three theories, in which higher-spin matter is coupled to electrodynamics, non-Abelian gauge theory, or gravity. The theories are chiral and have simple Lagrangians, resulting in Feynman rules analogous to those of massive scalars. Starting from these Feynman rules, we derive tree-level scattering amplitudes with two higher-spin matter particles and any number of positive-helicity photons, gluons, or gravitons. The amplitudes reproduce the arbitrary-multiplicity results that were obtained via on-shell recursion in a parity-conserving setting, and which chiral and nonchiral theories thus have in common. The presented theories are currently the only examples of consistent interacting field theories with massive higher-spin fields.

Gauging the Higher-Spin-Like Symmetries by the Moyal Product. II

Continuing the study of the Moyal Higher Spin Yang–Mills theory started in our previous paper we provide a detailed discussion of matter coupling and the corresponding tree-level amplitudes. We also start the investigation of the spectrum by expanding the master fields in terms of ordinary spacetime fields. We note that the spectrum can be consistent with unitarity while still preserving Lorentz covariance, albeit not in the usual way, but by employing an infinite-dimensional unitary representation of the Lorentz group.

Recent Developments of the Lauricella String Scattering Amplitudes and Their Exact SL(K + 3,C) Symmetry

In this review, we propose a new perspective to demonstrate the Gross conjecture regarding the high-energy symmetry of string theory. We review the construction of the exact string scattering amplitudes (SSAs) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory. These LSSAs form an infinite dimensional representation of the SL(K+3,C) group. Moreover, we show that the SL(K+3,C) group can be used to solve all the LSSAs and express them in terms of one amplitude. As an application in the hard scattering limit, the LSSA can be used to directly prove the Gross conjecture, which was previously corrected and proved by the method of the decoupling of zero norm states (ZNS). Finally, the exact LSSA can be used to rederive the recurrence relations of SSA in the Regge scattering limit with associated SL(5,C) symmetry and the extended recurrence relations (including the mass and spin dependent string BCJ relations) in the nonrelativistic scattering limit with the associated SL(4,C) symmetry discovered recently.