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

TL;DR

This paper investigates how T-duality transformations affect supersymmetry in type II supergravity, revealing that supersymmetry is preserved when Killing spinors are independent of the duality directions, and provides explicit formulas for SU(2) T-duality.

Contribution

It offers a detailed analysis of supersymmetry behavior under both Abelian and non-Abelian T-duality, including explicit expressions for SU(2) T-duality in symmetric spacetimes.

Findings

Supersymmetry variations relate before and after T-duality via the Kosmann Lie derivative.

Supersymmetry is preserved if Killing spinors are independent of T-duality directions.

Constructed a new AdS3 geometry with large N=(0,4) superconformal symmetry.

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.