Non-abelian T-duality of Pilch-Warner background

TL;DR

This paper derives the non-abelian T-dual of the Pilch-Warner supergravity background, preserving supersymmetry, and explores its properties through Fourier-Mukai transforms and Penrose limits.

Contribution

It provides the first explicit non-abelian T-dual of the Pilch-Warner background, including the dual metric, NS two-form, and R-R fields, while analyzing supersymmetry preservation and pp-wave limits.

Findings

Dual geometry preserves $ abla=1$ supersymmetry.

Explicit dual metric and NS two-form obtained.

Two pp-wave limits of the dual background analyzed.

Abstract

In this work we obtain the non-abelian T-dual geometry of the well-known Pilch-Warner supergravity solution in its infrared point. 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. The dual background preserves the $\mathcal{N}=1$ supersymmetry of the original one due to the fact that the Killing spinor does not depend on the directions on which the N-AT-D is performed. Finally, we consider two different pp-wave limits of the T-dual geometry by performing Penrose limits for two light-like geodesics.