Abstract
We initiate the classification of supersymmetric solutions of type II supergravity on R1,2×S3×M4. We find explicit local expressions for all backgrounds with either a single Killing spinor or two of equal norm, up to PDE's. We show that the only type II AdS×4S3 solution is the known N=4 AdS4 background obtained from the near-horizon limit of intersecting D2–D6 branes. Various known branes and intersecting brane systems are recovered, and we obtain a novel class of R1,2×S2×S3 solutions in IIA.
Highlights
The advent of the AdS-CFT correspondence has led to significant interest in the construction of Anti-de Sitter string backgrounds in various dimensions and with various amounts of supersymmetry
The Killing spinor equations reduce to constraints on the internal manifold, which can be solved by means of G-structure and generalised geometrical techniques
In addition to the case where the internal Killing spinors have equivalent norm, in section 6 we examine all backgrounds in the case where one of the Killing spinors vanishes, i.e., 2 = 0
Summary
The advent of the AdS-CFT correspondence has led to significant interest in the construction of Anti-de Sitter string backgrounds in various dimensions and with various amounts of supersymmetry. Solutions in this class are generically N = 2, from the Minkowski perspective, and support a SU (2) R-symmetry realised geometrically as one factor of the SO(4) SU (2)+ × SU (2)− isometry group manifold of S3 - the remaining SU (2) factor is a ”flavour” under which the Killing spinors are uncharged.1 This may sound strange as there is no 3d superconformal algebra with SU (2)R, but this only matters for solutions where R1,2 is part of a AdS4 factor so that SO(2, 3) is realised. Our other main result is the discovery of a new class of N = 4 solutions on R1,2 × S2 × S3 × Σ2 preserving an SO(4) R-symmetry but no AdS4 These generically have all possible IIA fluxes turned on and can be divided into cases either in massless or massive IIA at which point solutions are in one to one correspondence with a single PDE on Σ2. We discuss conventions and identities used, a mild extension of the 3+7 pure spinor equation construction (including the non-equivalent norm case), and a discussion on similar backgrounds from an M-theory perspective
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