Free fermion resolution of supergroup WZNW models

TL;DR

This paper develops a method to solve supergroup WZNW models by reducing them to bosonic subgroups, using a special representation and free fermion techniques, enabling analysis of their spectrum and correlation functions.

Contribution

It introduces a novel reduction technique for supergroup WZNW models to bosonic models, utilizing a Feigin-Fuchs type representation and free fermion construction.

Findings

Spectrum of the Laplacian on supergroups is non-diagonalizable.

Supergroup WZNW models exhibit logarithmic conformal field theory features.

Method applies to various supergroups including GL(M|N) and PSL(N|N).

Abstract

Extending our earlier work on PSL(2|2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M|N) along with several close relatives such as PSL(N|N), certain Poincare supergroups and the series OSP(2|2N). This remarkable progress relies on the use of a special Feigin-Fuchs type representation. In preparation for the field theory analysis, we shall exploit a minisuperspace analogue of a free fermion construction to deduce the spectrum of the Laplacian on type I supergroups. The latter is shown to be non-diagonalizable. After lifting these results to the full WZNW model, we address various issues of the field theory, including its modular invariance and the computation of correlation functions. In agreement with previous findings, supergroup WZNW models allow to study chiral and non-chiral aspects of logarithmic conformal field theory within a geometric framework. We shall briefly indicate how insights from WZNW models carry over to non-geometric examples, such as e.g. the W(p) triplet models.