Restricted sine-Gordon Theory in the Repulsive Regime as Perturbed Minimal CFTs

TL;DR

This paper constructs a restricted sine-Gordon model in the repulsive regime, linking it to minimal conformal field theories perturbed by a primary field, and verifies its properties via exact S-matrices and TBA analysis.

Contribution

It introduces a truncated sine-Gordon theory based on quantum group symmetry and connects it to perturbed minimal CFTs, providing exact S-matrices and central charge calculations.

Findings

Derived exact S-matrices for the particle spectrum.

Established the UV central charge matches minimal CFTs.

Connected the restricted sine-Gordon model to perturbed minimal models.

Abstract

We construct the restricted sine-Gordon theory by truncating the sine-Gordon multi-soliton Hilbert space for the repulsive coupling constant due to the quantum group symmetry $SL_q(2)$ which we identify from the Korepin's $S$-matrices. We connect this restricted sine-Gordon theory with the minimal ($c<1$) conformal field theory ${\cal M}_{p/p+2}$ ($p$ odd) perturbed by the least relevent primary field $\Phi_{1,3}$. The exact $S$-matrices are derived for the particle spectrum of a kink and neutral particles. As a consistency check, we compute the central charge of the restricted theory in the UV limit using the thermodynamic Bethe ansatz analysis and show that it is equal to that of ${\cal M}_{p/p+2}$.