Abstract
We investigate compactifications of type II and M-theory down to $AdS_5$ with generic fluxes that preserve eight supercharges, in the framework of Exceptional Generalized Geometry. The geometric data and gauge fields on the internal manifold are encoded in a pair of generalized structures corresponding to the vector and hyper-multiplets of the reduced five-dimensional supergravity. Supersymmetry translates into integrability conditions for these structures, generalizing, in the case of type IIB, the Sasaki-Einstein conditions. We show that the ten and eleven-dimensional type IIB and M-theory Killing-spinor equations specialized to a warped $AdS_5$ background imply the generalized integrability conditions.
Highlights
Flux compactifications play a central role both in the construction of phenomenologicallyrelevant models due to their potential to stabilize moduli, as well as in gauge/gravity duality where they realize duals of less symmetric gauge theories
We investigate compactifications of type II and M-theory down to AdS5 with generic fluxes that preserve eight supercharges, in the framework of Exceptional Generalized Geometry
In the generalized geometric language, metric degrees of freedom can be encoded in bilinears of spinors (this time transforming under the the compact subgroup of the duality group, namely USp(8) for the case of E6(6)), and these can be combined with the degrees of freedom of the gauge fields such that the corresponding objects transform in given representations of the Ed(d) group
Summary
Flux compactifications play a central role both in the construction of phenomenologicallyrelevant models due to their potential to stabilize moduli, as well as in gauge/gravity duality where they realize duals of less symmetric gauge theories. Compactifications leading to backgrounds with eight supercharges in the language of (exceptional) generalized geometry are characterized [5] by two generalized geometric structures that describe the hypermultiplet and vector multiplet structures of the lower dimensional supergravity theory. When this theory is five-dimensional, the generalized tangent bundle has reduced structure group USp(6) ⊂ USp(8) ⊂ E6(6) [11], where USp(8),. The generalized structures are written in terms of USp(8) bispinors These are subject to differential and algebraic conditions coming from the supersymmetry transformation of the internal and external gravitino (plus dilatino in the case of type IIB).
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