Duality Versus Supersymmetry and Compactification

TL;DR

This paper investigates how T-duality affects supersymmetry in compactified string theories, establishing conditions under which supersymmetry is preserved or broken in dual configurations.

Contribution

It proves that supersymmetry is preserved under T-duality if Killing spinors are independent of the isometry coordinate, providing criteria for supersymmetry preservation.

Findings

Supersymmetry preservation depends on Killing spinor independence.

Examples of supersymmetric and non-supersymmetric T-duals are provided.

Conditions for supersymmetry breaking in T-duality are identified.

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.