On non-abelian T-dual geometries with Ramond fluxes

TL;DR

The authors extend non-abelian T-duality to backgrounds with Ramond fluxes, showing that the duality can flip chirality when dualising an odd-dimensional isometry and yield massive IIA when appropriate RR forms are present, with the flip controlled by $\dim(G)$. They derive a general RR-flux transformation via a Lorentz rotation $\Lambda$ and spinor matrix $\Omega$, and apply it to SU(2) subgroups in $AdS_5\times S^5$ and $AdS_3\times S^3\times T^4$, obtaining AdS-preserving duals with reduced supersymmetry and an M-theory lift related to GM $\mathcal{N}=2$ backgrounds, suggesting a high-spin interpretation. They explicitly construct the dual NS and RR sectors, verify the massive IIA equations (with $m=\pm1$ in one case) or massless IIA in the D3 dual, and establish supersymmetry counts using dilatino/gravitino analyses and the Kosmann derivative, finding halves of the original supersymmetry are typically preserved. These results broaden the landscape of RR backgrounds accessible via non-abelian duality and connect holographic duals to high-spin sectors and GM-type geometries, with implications for AdS/CFT in new regimes.

Abstract

We show how to implement T-duality along non-abelian isometries in backgrounds with non-vanishing Ramond fields. When the dimension of the isometry group is odd (even) the duality swaps (preserves) the chirality of the theory. In certain cases a non-abelian duality can result in a massive type-IIA background. We provide two examples by dualising SU(2) isometry subgroups in $AdS_5\times S^5$ and $AdS_3\times S^3\times T^4$. The resultant dual geometries inherit the original AdS factors but have transverse spaces with reduced isometry and preserve only half of the original supersymmetry. The non-abelian dual of $AdS_5\times S^5$ has an M-theory lift which is related to the gravity duals of N=2 superconformal theories. We comment on a possible interpretation of this as a high spin limit.