Non-abelian T-duality of Pilch-Warner background

Abstract

In this work we obtain the non-abelian T-dual geometry of the well-known Pilch-Warner supergravity solution. We derive the dual metric and the NS two-form by gauging the isometry group of the initial theory and integrating out the introduced auxiliary gauge fields. Then we use the Fourier-Mukai transform from algebraic geometry to find the transformation rules of the R-R fields. Finally, we argue that the dual theory inherit the supersymmetry of the original one by considering the general dependence of the Killing spinor on the spacetime coordinates.