Criticality in self-dual sine-Gordon models

TL;DR

This paper investigates the critical behavior of self-dual sine-Gordon models at specific coupling values, revealing their relation to well-known universality classes like the three-state Potts model through non-perturbative methods.

Contribution

It provides a detailed analysis of the N=3 case, connecting the self-dual sine-Gordon model to Z3 criticality via integrable deformations and conformal field theory techniques.

Findings

The N=3 model exhibits Z3 universality class criticality.

Mapping to integrable deformations clarifies the infrared fixed points.

Connections to Wess-Zumino-Novikov-Witten models are established.

Abstract

We discuss the nature of criticality in the $\beta^2 = 2 \pi N$ self-dual extention of the sine-Gordon model. This field theory is related to the two-dimensional classical XY model with a N-fold degenerate symmetry-breaking field. We briefly overview the already studied cases $N=2,4$ and analyze in detail the case N=3 where a single phase transition in the three-state Potts universality class is expected to occur. The Z$_3$ infrared critical properties of the $\beta^2 = 6 \pi$ self-dual sine-Gordon model are derived using two non-perturbative approaches. On one hand, we map the model onto an integrable deformation of the Z$_4$ parafermion theory. The latter is known to flow to a massless Z$_3$ infrared fixed point. Another route is based on the connection with a chirally asymmetric, su(2)$_4$ $\otimes$ su(2)$_1$ Wess-Zumino-Novikov-Witten model with anisotropic current-current interaction, where we explore the existence of a decoupling (Toulouse) point.