On non-abelian T-dual geometries with Ramond fluxes

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

Holographic flows in non-Abelian T-dual geometries

“…In [21] it was shown that when a non-Abelian T-duality is applied to an SU(2) subgroup of isometries of the five-sphere in AdS 5 ×S 5 (or its Z 2 quotient) what results is a target space…”

“…This is rather more delicate since one needs to use an appropriate string theory formulation that incorporates the RR background fields. However, it was proposed in [21] that the transformation rules of the RR sector can be deduced using just knowledge of the NS-sector. The crucial point is that left and right movers on the world sheet have different transformation properties under the duality -viz.…”

“…can also be understood as a generalisation of the Fourier-Mukai transformations [26] and also gives rise to an action on supersymmetries [20,21,30].…”

“…Before moving to flowing geometries let us first look at AdS 5 × S 5 and comment on the relation between its non-Abelian T-dual, first worked out in [21], and geometries dual to Gaiotto QFTs [13].…”

“…Non-Abelian T-duality is the natural extension of T-duality of U(1) isometries to the case of non-Abelian isometry groups in target space and goes back to the pioneering work [15][16][17]. More recently, following the first implementation of non-Abelian T-duality in Ramond-Ramond backgrounds of supergravity [21], this has been actively exploited [22]- [43] as a solution generating tool of supergravity particularly in the context of the AdS/CF T correspondence.…”