Duality and restoration of 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 σ-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) ⊗ SL(2, R/U(1) and obtain a new exact 4-dim axionic instanton that generalizes the SU(2) ⊗ 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 σ-models with non-local N = 4 world-sheet supersymmetry.