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

TL;DR

The paper establishes a unifying criterion for supersymmetry preservation under both Abelian and SU(2) non-Abelian T-duality in type II supergravity: supersymmetry is preserved if the Kosmann spinorial Lie derivative along the duality directions vanishes, i.e., if Killing spinors are independent of those directions. It develops closed NS-sector and RR flux transformation rules for SU(2) T-duality in diagonal Bianchi IX backgrounds and validates them through explicit examples, including new AdS$_3$ geometries with extended superconformal symmetry. The Kosmann derivative thus encapsulates leading-order SUSY breaking under T-duality, enabling efficient assessment of preserved supersymmetry without full Killing spinor reconstruction. The work opens paths toward integrating non-Abelian T-duality with integrable deformations, double field theory, and Poisson-Lie dualities, and invites future study on $\alpha'$-corrections and holographic implications.

Abstract

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.