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

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.

v2: 57 pages, 1 figure, typos fixed and clarifications added, version to appear in JHEP

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• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
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• A Requiem for $Ad{S}_4\times \mathbb{C}{P}^3$ Fermionic self-T-duality
• Fermionic T-Duality of $Ad{S}_n\times S^n(\times S^n)\times T^m$ using IIA Supergravity
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• Dual conformal transformations of smooth holographic Wilson loops
• A study of integrable form factors in massless relativistic AdS_3
• Fermionic T-duality in massive type IIA supergravity on AdS_{10-k} x M_k
• T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory