Super non-abelian T-duality of principal chiral and coset models

Abstract

Super non-abelian T-duality of principal chiral and coset models on general Lie supergroups is analysed. We start from general principal chiral models, studying the OSp(1|2) case as a prime example and arguing that while the initial model is a proper three-dimensional supergravity background, its T-dual falls outside of this class. We then proceed by studying two families of coset models, namely symmetric and semi-symmetric spaces, highlighting where potential issues with T-duality may arise. In all these three classes of integrable models, dualisation along non-commuting bosonic and fermionic directions leads to the exchange of Maurer-Cartan equations with the equations of motion, so that integrability is preserved and the construction of T-dual Lax connections allowed.