Affine Algebras, $N{=}2$ Superconformal Algebras, and Gauged WZNW Models

TL;DR

This paper constructs a universal N=2 superconformal algebra within the BRST complex of affine Lie algebras, leading to new insights into gauged WZNW models and superconformal structures independent of matter representations.

Contribution

It introduces a canonical N=2 superconformal algebra applicable to any affine Lie algebra, independent of matter representations, and derives simplified master equations for supervirasoro constructions.

Findings

Universal N=2 SCA with fixed central charge for gauged WZNW models.

Associates each sl(2) embedding with a family of N=2 supervirasoro algebras.

Simplifies the equations governing generalized N=2 supervirasoro structures.

Abstract

We find a canonical $N{=}2$ superconformal algebra (SCA) in the BRST complex associated to any affine Lie algebra $\hat{\mathbf{h}}$ with $\mathbf{h}$ semisimple. In contrast with the similar known results for the Virasoro, $N{=}1$ supervirasoro, and $W_3$ algebras, this SCA does not depend on the particular "matter" representation chosen. Therefore it follows that every gauged WZNW model with data $(\mathbf{g}\supset\mathbf{h}, k)$ has an $N{=}2$ SCA with central charge $c=3\dim\mathbf{g}$ independent of the level $k$. In particular, this associates to every embedding $sl(2) \subset \mathbf{g}$ a one-parameter family of $c{=}9$ $N{=}2$ supervirasoro algebras. As a by-product of the construction, one can deduce a new set of "master equations" for generalized $N{=}2$ supervirasoro constructions which is simpler than the one considered thus far.