Duality Versus Supersymmetry and Compactification

TL;DR

This paper establishes a precise criterion for when T-duality preserves supersymmetry in the presence of a Killing vector: unbroken supersymmetry is maintained if and only if the Killing spinors are independent of the coordinate along the dualized isometry, with the Killing spinor transforming simply under duality. By performing a detailed dimensional reduction of N=1, d=10 supergravity and deriving duality-invariant nine-dimensional spinor equations, the authors connect the geometric independence of Killing spinors to the algebraic action of Buscher duality. They illustrate the criterion with explicit Loser and Winner examples, including SSW/GFS and CHS/multimonopole/stringy ALE instanton pairs, and discuss time-like duality and supersymmetric truncations to d=4. The results clarify when T-duality can be used to generate new SUSY-preserving solutions and explain observed counterexamples, with implications for α′-corrected dualities and higher-dimensional constructions.

Abstract

We study the interplay between T-duality, compactification and supersymmetry. We prove that when the original configuration has unbroken space-time supersymmetries, the dual configuration also does if a special condition is met: the Killing spinors of the original configuration have to be independent on the coordinate which corresponds to the isometry direction of the bosonic fields used for duality. Examples of ``losers" (T-duals are not supersymmetric) and ``winners" (T-duals are supersymmetric) are given.