Poisson-Lie T-dual sigma models on supermanifolds

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.

13 pages, Revised and accepted for publication in JHEP

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Cited by in corpus (21)

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• Classification of two and three dimensional Lie super-bialgebras
• Super Poisson-Lie symmetry of the GL(1|1) WZNW model and worldsheet boundary conditions
• String cosmology from Poisson-Lie T-dual sigma models on supermanifolds
• Super Non-Abelian T-Duality
• WZW models as mutual super Poisson-Lie T-dual sigma models
• Open effective theory of scalar field in rotating plasma
• Classification of four and six dimensional Drinfel'd superdoubles
• Generalized Dualities and Supergroups
• The gl(1|1) Lie superbialgebras
• Jacobi-Lie symmetry and Jacobi-Lie T-dual sigma models on group manifolds
• Classical r-matrices of two and three dimensional Lie super-bialgebras and their Poisson-Lie supergroups
• Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3+A)$
• Cosmological string backgrounds from super Poisson-Lie T-plurality
• A hierarchy of WZW models related to super Poisson-Lie T-duality
• T-dualization of Gödel string cosmologies via Poisson-Lie T-duality approach
• Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-duality
• T-duality/plurality of BTZ black hole metric coupled to two fermionic fields
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Yang-Baxter deformations of the OSP(1|2) WZW model