AdS2 × S6 versus AdS6 × S2 in Type IIB supergravity

Abstract

Abstract We obtain the complete local solutions with 16 supersymmetries to Type IIB supergravity on a space-time of the form AdS2 × S 6 warped over a Riemann surface Σ in terms of two locally holmorphic functions on Σ. We construct the general Ansatz for the bosonic supergravity fields and supersymmetry generators compatible with the SO(2, 1) ⊕ SO(7) isometry algebra of space-time, which extends to the corresponding real form of the exceptional Lie superalgebra F (4). We reduce the BPS equations to this Ansatz, obtain their general local solutions, and show that these local solutions solve the full Type IIB supergravity field equations and Bianchi identities. We contrast the AdS2 × S 6 solution with the closely related AdS6 × S 2 case and present our results for both in parallel. Finally, we present a preliminary analysis of positivity and regularity conditions for AdS2 × S 6, but postpone the construction of globally regular solutions to a subsequent paper.