T-Duality of Green-Schwarz Superstrings on AdS(d) x S(d) x M(10-2d)

TL;DR

This paper demonstrates the self-duality of Green-Schwarz superstring models on various AdS and sphere backgrounds under combined T-dualities, extending to supergravity backgrounds with Ramond-Ramond fluxes, without gauge fixing kappa symmetry.

Contribution

It proves T-self-duality of supercoset sigma models and superstrings on AdS$_d imes S^d$ backgrounds, including non-supercoset modes and supergravity fields, without gauge fixing kappa symmetry.

Findings

Self-duality verified for supercoset sigma models on AdS$_d imes S^d$ (d=2,3,5).

Evidence for T-self-duality of full superstring theory on AdS$_d imes S^d imes T^{10-2d}$.

Supergravity analysis confirms T-self-duality of entire backgrounds with Ramond-Ramond fluxes.

Abstract

We verify the self-duality of Green-Schwarz supercoset sigma models on AdS$_d \times S^d $ backgrounds (d=2,3,5) under combined bosonic and fermionic T-dualities without gauge fixing kappa symmetry. We also prove this property for superstrings on AdS$_d \times S^d \times S^d$ (d=2,3) described by supercoset sigma models with the isometries governed by the exceptional Lie supergroups $D(2,1;\alpha)$ (d=2) and $D(2,1;\alpha)\times D(2,1;\alpha)$ (d=3), which requires an additional T-dualisation along one of the spheres. Then, by taking into account the contribution of non-supercoset fermionic modes (up to the second order), we provide evidence for the T-self-duality of the complete type IIA and IIB Green-Schwarz superstring theory on AdS$_d\times S^d \times T^{10-2d}$ (d=2,3) backgrounds with Ramond-Ramond fluxes. Finally, applying the Buscher-like rules to T-dualising supergravity fields, we prove the T-self-duality of the whole class of the AdS$_d\times S^d \times M^{10-2d}$ superbackgrounds with Ramond-Ramond fluxes in the context of supergravity.