Correspondences between WZNW models and CFTs with W-algebra symmetry

TL;DR

This paper explores the deep connections between WZNW models on (super-)groups and W-algebra symmetric conformal field theories, revealing how their correlation functions relate through algebraic reductions and embeddings.

Contribution

It establishes explicit correspondences between WZNW models and W-algebra CFTs using Drinfeld-Sokolov reduction and algebra embeddings, extending to supergroups and various Lie algebra partitions.

Findings

Correlation functions of WZNW models expressed via W-algebra CFT correlators

Explicit construction of W-algebras from affine sl(N) using sl(2) embeddings

Analysis of supergroup extensions and specific algebra partitions

Abstract

We study theories with W-algebra symmetries and their relation to WZNW models on (super-)groups. Correlation functions of the WZNW models are expressed in terms of correlators of CFTs with W-algebra symmetry. The symmetries of the theories involved in these correspondences are related by the Drinfeld-Sokolov reduction of Lie algebras to W-algebras. The W-algebras considered in this paper are the Bershadsky-Polyakov algebra for sl(3) and the quasi-superconformal algebra for generic sl(N|M). The quantum W-algebras obtained from affine sl(N) are constructed using embeddings of sl(2) into sl(N), and these can in turn be characterized by partitions of N. The above cases correspond to \underline{N+2} = \underline{2} + N \underline{1} and its supergroup extension. Finally, sl(2N) and the correspondence corresponding to \underline{2N} = N \underline{2} is also analyzed.