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

Changrim Ahn

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

Changrim Ahn

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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 $Φ_{1,3}$. 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 ${\cal M}_{p/p+2}$.

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Changrim Ahn. 1991-11-11. Restricted sine-Gordon Theory in the Repulsive Regime as Perturbed Minimal CFTs. https://arxiv.org/abs/hep-th/9111022

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