The Sine-Gordon Model as $\SO(n)_{1} \times \SO(n)_{1} \over \SO(n)_{2}$ Perturbed Coset Theory and Generalizations

TL;DR

This paper explores the relationships between perturbed coset theories and sine-Gordon models, extending previous results to new algebraic cases, analyzing Bethe Ansatz solutions, and proposing TBA equations for a broad class of models involving non-simply-laced groups.

Contribution

It extends the analysis of perturbed coset theories to $ ext{SO}(2n-1)$ cases, analyzes the algebraic Bethe Ansatz for special points, and proposes TBA equations for generalized models with non-simply-laced groups.

Findings

Ground states of certain coset theories match sine-Gordon models at special couplings.

Established a duality between theories in the attractive and repulsive regimes.

Proposed TBA systems for a wide class of perturbed coset models involving non-simply-laced groups.

Abstract

The ground state of the $\SO(2n)_{1} \times \SO(2n)_{1} \over \SO(2n)_{2}$ coset theories, perturbed by the $\phi^{id,id}_{adj}$ operator and those of the sine-Gordon theory, for special values of the coupling constant in the attracting regime, is the same. In the first part of this paper we extend these results to the $\SO(2n-1)$ cases. In the second part, we analyze the Algebraic Bethe Ansatz procedure for special points in the repulsive region. We find a one-to-one ``duality'' correspondence between these theories and those studied in the first part of the paper. We use the gluing procedure at the massive node proposed by Fendley and Intriligator in order to obtain the TBA systems for the generalized parafermionic supersymmetric sine-Gordon model. In the third part we propose the TBA equations for the whole class of perturbed coset models $G_k \times G_l \over G_{k+l}$ with the operator $\phi^{id,id}_{adj}$ and $G$ a non-simply-laced group generated by one of the $\G_2,\F_4,\B_n,\C_n$ algebras.