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

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 $S{L}_q(2)$ which we identify from the Korepin's $S$-matrices. We connect this restricted sine-Gordon theory with the minimal ($c<1$) conformal field theory ${\mathcal{M}}_{p/p+2}$ ($p$ 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 ${\mathcal{M}}_{p/p+2}$.

34 Pages