Conformal Current Algebra in Two Dimensions

TL;DR

This paper constructs a conformal non-chiral current algebra in two dimensions within supergroup sigma-models, providing exact computations and establishing connections to quantum integrability and string theory applications.

Contribution

It introduces a non-chiral current algebra in 2D conformal models on supergroups with vanishing dual Coxeter number, using two methods for exact current algebra derivation.

Findings

Exact two- and three-point functions of currents computed.

Current algebra realized as a non-chiral Kac-Moody algebra.

Constructed commuting operators closed under Kac-Moody action.

Abstract

We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing dual Coxeter number, with or without a Wess-Zumino term. The current algebra is computed using two distinct methods. First we exploit special algebraic properties of supergroups to compute the exact two- and three-point functions of the currents and from them we infer the current algebra. The algebra is also calculated by using conformal perturbation theory about the Wess-Zumino-Witten point and resumming the perturbation series. We also prove that these models realize a non-chiral Kac-Moody algebra and construct an infinite set of commuting operators that is closed under the action of the Kac-Moody generators. The supergroup models that we consider include models with applications to statistical mechanics, condensed matter and string theory. In particular, our results may help to systematically solve and clarify the quantum integrability of PSU(n|n) models and their cosets, which appear prominently in string worldsheet models on anti-deSitter spaces.