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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    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.

Non‐abelian T‐duality of Pilch‐Warner background