Exact mass gap of the chiral SU(n) x SU(n) model

Large-N Principal Chiral Model in Arbitrary External Fields

We report the explicit solution for the vacuum state of the two-dimensional SU(N) principal chiral model at large N for an arbitrary set of chemical potentials and any interaction strength, a unique result of such kind for an asymptotically free quantum field theory. The solution matches one-loop perturbative calculation at weak coupling, and in the opposite strong-coupling regime exhibits an emergent spacial dimension from the continuum limit of the SU(N) Dynkin diagram.

Double-Scaling Limit in the Principal Chiral Model: A New Noncritical String?

We initiate a systematic, non-perturbative study of the large-N expansion in the two-dimensional SU(N)×SU(N) principal Chiral model (PCM). Starting with the known infinite-N solution for the ground state at fixed chemical potential, we devise an iterative procedure to solve the Bethe ansatz equations order by order in 1/N. The first few orders, which we explicitly compute, reveal a systematic enhancement pattern at strong coupling calling for the near-threshold resummation of the large-N expansion. The resulting double-scaling limit bears striking similarities to the c=1 noncritical string theory and suggests that the double-scaled PCM is dual to a noncritical string with a (2+1)-dimensional target space where an additional dimension emerges dynamically from the SU(N) Dynkin diagram.

Exact Mass-Coupling Relation for the Homogeneous Sine-Gordon Model

We derive the exact mass-coupling relation of the simplest multiscale quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass scales. The relation is obtained by comparing the perturbed conformal field theory description of the model valid at short distances to the large distance bootstrap description based on the model's integrability. In particular, we find a differential equation for the relation by constructing conserved tensor currents, which satisfy a generalization of the Θ sum rule Ward identity. The mass-coupling relation is written in terms of hypergeometric functions.