Geometry of branes on supergroups

TL;DR

This paper explores the geometry of branes in supergroup WZNW models, revealing that their worldvolumes are typically twisted superconjugacy classes and identifying new atypical branes linked to atypical representations.

Contribution

It introduces the concept of new atypical branes in supergroup models and connects their geometry to affine Lie superalgebra representations.

Findings

Branes are generally twisted superconjugacy classes.

A new class of atypical branes arises when fermionic directions are not fully delocalized.

Atypical branes are associated with atypical representations of affine Lie superalgebras.

Abstract

In this note we analyze the geometry of maximally symmetric boundary conditions in Lie supergroup Wess-Zumino-Novikov-Witten models. We find that generically the worldvolume of a brane is a twisted superconjugacy class, very much like in the Lie group case. Whenever the brane is not completely delocalized in the fermionic directions a new atypical class of branes arises. We give an example of these new branes and show for type I supergroups and trivial gluing conditions that they can be naturally associated with atypical representations of the affine Lie superalgebra.