JT gravity from non-Abelian T-duality

Abstract

We study the geometries obtained by performing super non-Abelian T-duality of the Principal Chiral Model on OSp(1|2). While the initial model represents an appropriate 3D supergravity background, interpretable as the superspace version of AdS3, the T-dual model fails solving the 3D supergravity torsion constraints. We argue that this has to do with a factorisation pattern taking place under dualisation: the dual 3D geometry can be rewritten as the supersymmetric version of AdS2, satisfying the supergravity constraints, fibered over what we interpret as the superspace equivalent of the standard bosonic line. We discuss an interesting connection between T-duals of generic Principal Chiral Models and Poisson sigma models. We exploit it to show that in a suitable limit the dual action studied in this work gives rise to JT (super)gravity.