Constructing Infinite Particle Spectra

TL;DR

This paper introduces a construction method for infinite particle spectra in scattering matrices, generalizing hyperbolic models to elliptic cases, with applications to affine Toda and sine-Gordon theories, and computes related RG flows.

Contribution

It presents a novel approach to include infinite resonance states in scattering matrices, extending hyperbolic models to elliptic ones, and provides explicit RG analysis for these theories.

Findings

New elliptic S-matrices generalizing hyperbolic models

Explicit RG flow functions for generalized sinh-Gordon model

Identification of UV conformal field theory central charges

Abstract

We propose a general construction principle which allows to include an infinite number of resonance states into a scattering matrix of hyperbolic type. As a concrete realization of this mechanism we provide new S-matrices generalizing a class of hyperbolic ones, which are related to a pair of simple Lie algebras, to the elliptic case. For specific choices of the algebras we propose elliptic generalizations of affine Toda field theories and the homogeneous sine-Gordon models. For the generalization of the sinh-Gordon model we compute explicitly renormalization group scaling functions by means of the c-theorem and the thermodynamic Bethe ansatz. In particular we identify the Virasoro central charges of the corresponding ultraviolet conformal field theories.