Super Poisson-Lie symmetry of the GL(1|1) WZNW model and worldsheet boundary conditions

TL;DR

This paper explores super Poisson-Lie symmetry in the GL(1|1) WZNW model, analyzes boundary conditions for D-branes on supermanifolds, and derives dual gluing supermatrices using super Poisson-Lie T-duality.

Contribution

It demonstrates super Poisson-Lie symmetry in the GL(1|1) WZNW model and provides explicit formulas for dual boundary conditions and gluing supermatrices.

Findings

Identified super Poisson-Lie symmetry in the model

Derived dual gluing supermatrix formulas

Analyzed boundary conditions for D-branes

Abstract

We show that the WZNW model on the Lie supergroup GL(1|1) has super Poisson-Lie symmetry with the dual Lie supergroup B + A + A1;1|.i. Then, we discuss about D-branes and worldsheet boundary conditions on supermanifolds, in general, and obtain the algebraic relations on the gluing supermatrix for the Lie supergroup case. Finally, using the supercanonical transformation description of the super Poisson-Lie T-duality transformation, we obtain formula for the description of the dual gluing supermatrix, then, we find the gluing supermatrix for the WZNW model on GL(1|1) and its dual model. We also discuss about different boundary conditions.