Massive Symmetric Space sine-Gordon Soliton Theories and Perturbed Conformal Field Theory

TL;DR

This paper identifies the conformal field theories related to massive symmetric space sine-Gordon models, establishes their quantum integrability, and explores their soliton spectrum, including explicit solutions and charge properties.

Contribution

It connects symmetric space sine-Gordon theories with perturbed conformal field theories and proves quantum integrability for a class of models called Split models.

Findings

Quantum conserved charges of spin +3 and -3 are shown for Split models.

Explicit soliton solutions with topological and Noether charges are constructed.

Theories are confirmed to be quantum integrable, supporting the existence of a factorizable S-matrix.

Abstract

The perturbed conformal field theories corresponding to the massive Symmetric Space sine-Gordon soliton theories are identified by calculating the central charge of the unperturbed conformal field theory and the conformal dimension of the perturbation. They are described by an action with a positive-definite kinetic term and a real potential term bounded from below, their equations of motion are non-abelian affine Toda equations and, moreover, they exhibit a mass gap. The unperturbed CFT corresponding to the compact symmetric space G/G_0 is either the WZNW action for G_0 or the gauged WZNW action for a coset of the form G_0/U(1)^p. The quantum integrability of the theories that describe perturbations of a WZNW action, named Split models, is established by showing that they have quantum conserved quantities of spin +3 and -3. Together with the already known results for the other massive theories associated with the non-abelian affine Toda equations, the Homogeneous sine-Gordon theories, this supports the conjecture that all the massive Symmetric Space sine-Gordon theories will be quantum integrable and, hence, will admit a factorizable S-matrix. The general features of the soliton spectrum are discussed, and some explicit soliton solutions for the Split models are constructed. In general, the solitons will carry both topological charges and abelian Noether charges. Moreover, the spectrum is expected to include stable and unstable particles.