Non-abelian T-duality in superspace

Abstract

Super non-abelian T-duality of principal chiral and coset models on general Lie supergroups is analysed. We start from 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. 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. Potential impediments arise in the dualisation procedure of coset models when integrating out the gauge fields in favour of the dual variables. This process cannot be performed in general and we isolate the obstruction, briefly discussing two examples in which a solution can be found.

This is a pre-viva talk by Danielle Bielli in the Fields, Strings, and Geometry Group at Surrey.