English

Poisson-Lie T-dual sigma models on supermanifolds

High Energy Physics - Theory 2009-10-02 v3

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,D10p=1/2)((2A1,1 + 2A)^1, D10_p=1/2) and ((2A1,1+2A)1,I)((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.

Keywords

Cite

@article{arxiv.0901.1592,
  title  = {Poisson-Lie T-dual sigma models on supermanifolds},
  author = {A. Eghbali and A. Rezaei-Aghdam},
  journal= {arXiv preprint arXiv:0901.1592},
  year   = {2009}
}

Comments

13 pages, Revised and accepted for publication in JHEP

R2 v1 2026-06-21T11:59:50.492Z