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

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.

13 pages, Plain TeX, BONN-HE-93-20. (A note added and a minor change at the end of section 3; v4: solved legacy compilation problems)

References in corpus (1)

• d\leq1\bigcup d\geq25$andConstrainedKPHierarchyfromBRSTInvarianceinthe$c\neq3$ Topological Algebra

Cited by in corpus (5)

• Irrational Conformal Field Theory
• Nonreductive WZW models and their CFTs
• Nonreductive WZW models and their CFTs, II: N=1 and N=2 cosets
• N=2 structures in all string theories
• The BRST quantisation of chiral BMS-like field theories