Branes in the GL(1|1) WZNW-Model

TL;DR

This paper systematically studies boundary conditions in the GL(1|1) WZNW model, identifying all maximally symmetric branes and demonstrating that key algebraic features of boundary theories extend to this non-rational logarithmic conformal field theory.

Contribution

It provides a complete classification of maximally symmetric branes in the GL(1|1) WZNW model, including their geometric and algebraic properties, extending boundary theory concepts to a non-rational setting.

Findings

Identified a unique maximal super-dimension brane.

Discovered a 2-parameter family of super-dimension 0|2 branes.

Found an infinite set of localized branes with a single modulus.

Abstract

We initiate a systematic study of boundary conditions in conformal field theories with target space supersymmetry. The WZNW model on GL(1|1) is used as a prototypical example for which we find the complete set of maximally symmetric branes. This includes a unique brane of maximal super-dimension 2|2, a 2-parameter family of branes with super-dimension 0|2 and an infinite set of fully localized branes possessing a single modulus. Members of the latter family can only exist along certain lines on the bosonic base, much like fractional branes at orbifold singularities. Our results establish that all essential algebraic features of Cardy-type boundary theories carry over to the non-rational logarithmic WZNW model on GL(1|1).