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Supersymmetry and non-Abelian T-duality in type II supergravity

We study the effect of T-duality on supersymmetry in the context of type II supergravity. For both U(1) Abelian and SU(2) non-Abelian T-duality, we demonstrate that the supersymmetry variations after T-duality are related to the variations before T-duality through the Kosmann spinorial Lie derivative, which vanishes when the Killing spinors are independent of the T-duality directions. As a byproduct of our analysis, we present closed expressions for SU(2) T-duality in a class of spacetimes with diagonal Bianchi IX symmetry and comment on specific examples of T-dual geometries, including a novel AdS3 geometry with large N = (0,4) superconformal symmetry.