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Non-abelian T-duality of Pilch-Warner background

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.