WZW models as mutual super Poisson-Lie T-dual sigma models

TL;DR

This paper constructs a WZW model on a Lie supergroup, demonstrating its super Poisson-Lie symmetry and showing that the dual model retains the same structure, preserving N=(2,2) supersymmetry under T-duality.

Contribution

It introduces a WZW model on a specific Lie supergroup with super Poisson-Lie symmetry and proves the preservation of supersymmetry under T-duality due to isomorphism with a Manin supertriple.

Findings

The model exhibits super Poisson-Lie symmetry with a dual Lie supergroup.

The dual model is equivalent to a WZW model on an isomorphic supergroup.

N=(2,2) structure is preserved under super Poisson-Lie T-duality.

Abstract

A WZW model on the Lie supergroup (C3+A) is constructed. It is shown that this model contains super Poisson-Lie symmetry with the dual Lie supergroup C3 + A1,1|.i. Furthermore, we show that the dual model is also equivalent to the WZW model on isomorphic Lie supergroup (C3+A).i. In this manner, because of isomorphism of the (C3+A) with a Manin supertriple, it is shown that the N=(2,2) structure is preserved under the super Poisson-Lie T-duality transformation.