Non-abelian T-duality of Pilch-Warner background

Understand

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.