Searching for new homogeneous sine-Gordon theories using T-duality symmetries

TL;DR

This paper explores the use of T-duality symmetries to identify new homogeneous sine-Gordon theories related to specific cosets, revealing potential additional theories for certain Lie groups.

Contribution

It introduces a method to find new HSG theories via T-duality, uncovering previously unconsidered theories for certain Lie groups.

Findings

Potential existence of two non-equivalent HSG theories for G=SU(n), n≥5, and E6.

Identification of different phases of HSG theories through T-duality.

Suggestion of new HSG theories not previously studied.

Abstract

The Homogeneous sine-Gordon (HSG) theories are integrable perturbations of $G_k/U(1)^{r_G}$ coset CFTs, where $G$ is a simple compact Lie group of rank $r_G$ and $k>1$ is an integer. Using their T-duality symmetries, we investigate the relationship between the different theories corresponding to a given coset, and between the different phases of a particular theory. Our results suggest that for $G=SU(n)$ with $n\geq5$ and $E_6$ there could be two non-equivalent HSG theories associated to the same coset, one of which has not been considered so far.