Branes in Supergroups

TL;DR

This thesis systematically studies branes in supergroup WZNW models, revealing their worldvolumes as twisted superconjugacy classes, constructing boundary states, and analyzing their correlation functions, including logarithmic singularities.

Contribution

It provides a comprehensive analysis of branes in supergroup WZNW models, including explicit boundary state constructions and correlation function computations, with new insights into their supersymmetric properties.

Findings

Branes' worldvolume is a twisted superconjugacy class.

Explicit boundary states for GL(1|1) model are constructed.

Logarithmic singularities are found in correlation functions.

Abstract

In this thesis we initiate a systematic study of branes in Wess-Zumino-Novikov-Witten models with Lie supergroup target space. We start by showing that a branes' worldvolume is a twisted superconjugacy class and construct the action of the boundary WZNW model. Then we consider symplectic fermions and give a complete description of boundary states including twisted sectors. Further we show that the GL(1|1) WZNW model is equivalent to symplectic fermions plus two scalars. We then consider the GL(1|1) boundary theory. Twisted and untwisted Cardy boundary states are constructed explicitly and their amplitudes are computed. In the twisted case we find a perturbative formulation of the model. For this purpose the introduction of an additional fermionic boundary degree of freedom is necessary. We compute all bulk one-point functions, bulk-boundary two-point functions and boundary three-point functions. Logarithmic singularities appear in bulk-boundary as well as pure boundary correlation functions. Finally we turn to world-sheet and target space supersymmetric models. There is N=2 superconformal symmetry in many supercosets and also in certain supergroups. In the supergroup case we find some branes that preserve the topological A-twist and some that preserve the B-twist.