T-duality of Green-Schwarz superstrings on AdSd x S d x M 10-2d

We verify the self-duality of Green-Schwarz supercoset sigma models on AdS(d) x 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) x S-d x 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) x 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) x S-d x T10-2d (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) x S-d x M10-2d superbackgrounds with Ramond-Ramond fluxes in the context of supergravity.