Abstract
We obtain the complete local solutions with 16 supersymmetries to Type IIB supergravity on a space-time of the form AdS2 × S6 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 × S6 solution with the closely related AdS6 × S2 case and present our results for both in parallel. Finally, we present a preliminary analysis of positivity and regularity conditions for AdS2 × S6, but postpone the construction of globally regular solutions to a subsequent paper.
Highlights
Half-BPS solutions to Type IIB supergravity were obtained recently for a space-time of the form AdS6 × S2 warped over a Riemann surface [1,2,3,4].1 The motivation for that work was the construction of holographic duals to five-dimensional superconformal field theories (SCFTs)
We obtain the complete local solutions with 16 supersymmetries to Type IIB supergravity on a space-time of the form AdS2 × S6 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)
Summary
Half-BPS solutions to Type IIB supergravity were obtained recently for a space-time of the form AdS6 × S2 warped over a Riemann surface [1,2,3,4].1 The motivation for that work was the construction of holographic duals to five-dimensional superconformal field theories (SCFTs). We verify that the full set of Type IIB field equations are satisfied when the bosonic supergravity fields are given by the solutions to the BPS equations and axiondilaton Bianchi identities We show this for the AdS2 × S6 and AdS6 × S2 cases in parallel, and provide this check for the solutions constructed in [1]. We discuss the possibility of performing a “double analytic continuation” of the global AdS6 × S2 solutions constructed in [2, 3] to the present case of AdS2 × S6 Such continuations are found to satisfy the field equations, they appear to be neither supersymmetric nor physically regular. We begin by reviewing the salient features of Type IIB supergravity needed in this paper, and obtain the SO(2, 1) ⊕ SO(7)-invariant Ansatz for the bosonic supergravity fields and the generator of supersymmetry transformations
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