Nonreductive WZW models and their CFTs

TL;DR

This paper explores nonreductive WZW models with bi-invariant metrics, linking them to nonreductive Sugawara constructions, coset models, and their applications in string theory and topological CFTs.

Contribution

It introduces a framework for nonreductive WZW models, connects them to affine Sugawara constructions, and analyzes their gauged versions and topological aspects.

Findings

Gauging diagonal subgroups yields conformal coset models.

Identifies Kazama algebra extending BRST in topological CFT.

Constructs exact string backgrounds from nonreductive WZW models.

Abstract

We study two-dimensional WZW models with target space a nonreductive Lie group. Such models exist whenever the Lie group possesses a bi-invariant metric. We show that such WZW models provide a lagrangian description of the nonreductive (affine) Sugawara construction. We investigate the gauged WZW models and we prove that gauging a diagonal subgroup results in a conformal field theory which can be identified with a coset construction. A large class of exact four-dimensional string backgrounds arise in this fashion. We then study the topological conformal field theory resulting from the $G/G$ coset. We identify the Kazama algebra extending the BRST algebra, and the BV algebra structure in BRST cohomology which it induces.