Supersymmetric AdS_5 solutions of M-theory

TL;DR

This paper classifies supersymmetric AdS_5 solutions in M-theory, revealing new explicit geometries involving complex manifolds and connections to Sasaki-Einstein spaces, expanding the landscape of known supergravity solutions.

Contribution

It provides the most general classification of supersymmetric AdS_5 solutions in M-theory with explicit constructions and links to known geometries like Sasaki-Einstein spaces.

Findings

Found a large family of explicit regular solutions with compact complex manifolds.

Identified connections between solutions and Sasaki-Einstein spaces, including T^{1,1}/Z_2.

Classified solutions involving warped products with specific geometric structures.

Abstract

We analyse the most general supersymmetric solutions of D=11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M_6, with four-form flux on M_6. We show that M_6 is partly specified by a one-parameter family of four-dimensional Kahler metrics. We find a large family of new explicit regular solutions where M_6 is a compact, complex manifold which is topologically a two-sphere bundle over a four-dimensional base, where the latter is either (i) Kahler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T^{1,1}/Z_2. Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.