Duality and Restoration of Manifest Supersymmetry

TL;DR

This paper explores how T-duality can restore manifest supersymmetry in string backgrounds by transforming non-local supersymmetries into local ones, with detailed examples and conditions for preservation of supersymmetry.

Contribution

It provides general conditions for non-local supersymmetry in 2D N=1 sigma-models and demonstrates how T-duality can restore manifest supersymmetry, including new exact solutions and theoretical theorems.

Findings

T-duality can convert non-local supersymmetries into local ones.

Derived conditions for T-duality to preserve N=4 supersymmetry.

Presented a new exact 4D axionic instanton with manifest supersymmetry.

Abstract

World-sheet and spacetime supersymmetries that are manifest in some string backgrounds may not be so in their T-duals. Nevertheless, they always remain symmetries of the underlying conformal field theory. In previous work the mechanism by which T-duality destroys manifest supersymmetry and gives rise to non-local realizations was found. We give the general conditions for a 2-dim N=1 supersymmetric sigma-model to have non-local and hence non-manifest extended supersymmetry. We then examine T-duality as a mechanism of restoring manifest supersymmetry. This happens whenever appropriate combinations of non-local parafermions of the underlying conformal field theory become local due to non-trivial world-sheet effects. We present, in detail, an example arising from the model SU(2)/U(1) X SL(2,R)/U(1) and obtain a new exact 4-dim axionic instanton, that generalizes the SU(2) X U(1) semi-wormhole, and has manifest spacetime as well as N=4 world-sheet supersymmetry. In addition, general necessary conditions for abelian T-duality to preserve manifest N=4 world-sheet supersymmetry are derived and applied to WZW models based on quaternionic groups. We also prove some theorems for sigma-models with non-local N=4 world-sheet supersymmetry.