Poisson-Lie T-dual sigma models on supermanifolds

TL;DR

This paper explores Poisson-Lie symmetry in T-dual sigma models on supermanifolds, establishing conditions for symmetry integrability and illustrating how duality swaps fermionic and bosonic fields.

Contribution

It demonstrates the equivalence of super Poisson-Lie symmetry integrability with super Jacobi identities and analyzes duality effects on field roles in supermanifold models.

Findings

Super Poisson-Lie symmetry integrability is equivalent to super Jacobi identities.

T-duality swaps fermionic and bosonic fields in Abelian supermanifold models.

Explicit examples involve four-dimensional Lie super-bialgebras.

Abstract

We investigate Poisson-Lie symmetry for T-dual sigma models on supermanifolds in general and on Lie supergroups in particular. We show that the integrability condition on this super Poisson-Lie symmetry is equivalent to the super Jacobi identities of the Lie super-bialgebras. As examples we consider models related to four dimensional Lie super-bialgebras $((2A1,1 + 2A)^1, D10_p=1/2)$ and $((2A1,1 + 2A)^1, I)$. Then generally it is shown that for Abelian case (g, I) the super Poisson-Lie T-duality transforms the role of fermionic (bosonic) fields in the model to bosonic (fermionic) fields on the dual model and vice versa.