T-duality and world-sheet supersymmetry

TL;DR

This paper investigates how T-duality transformations affect world-sheet supersymmetry in four-dimensional string backgrounds, revealing that N=4 supersymmetry is generally broken to N=2 under Abelian and non-Abelian dualities, with non-local realizations emerging.

Contribution

It demonstrates the conditions under which extended world-sheet supersymmetry is preserved or broken by T-duality, highlighting the role of local and non-local supersymmetry realizations.

Findings

N=2 supersymmetry always preserved under Abelian T-duality.

N=4 supersymmetry breaks to N=2 in rotational cases.

Extended supersymmetries cannot be preserved under non-Abelian duality for certain metrics.

Abstract

Four-dimensional string backgrounds with local realizations of N = 4 world-sheet supersymmetry have, in the presence of a rotational Killing symmetry, only one complex structure which is an SO(2) singlet, while the other two form an SO(2) doublet. Although N = 2 world-sheet supersymmetry is always preserved under Abelian T-duality transformations, N = 4 breaks down to N = 2 in the rotational case. A non-local realization of N = 4 supersymmetry emerges, instead, with world-sheet parafermions. For SO(3)-invariant metrics of purely rotational type, like the Taub-NUT and the Atiyah-Hitchin metrics, none of the locally realized extended world-sheet supersymmetries can be preserved under non-Abelian duality.