Supersymmetric AdS_5 solutions of M-theory

TL;DR

The paper addresses the problem of finding and classifying all supersymmetric AdS5 solutions in M-theory with warp factors and flux, expressing the internal geometry M6 via a G-structure (SU(2)) framework and a Killing vector that encodes the R-symmetry.The authors derive a complete set of local differential conditions, show they imply the equations of motion, and identify a global construction where M6 is a CP^1 bundle over a 4D Kahler base, with the base constrained to be KE (positive curvature) or a product of two constant-curvature surfaces.They construct large families of explicit regular solutions, including S^2 fibrations over KE bases and over products of Riemann surfaces, and demonstrate that these M-theory backgrounds yield IIA and IIB duals (via circle reductions and T-duality) that include new Sasaki-Einstein spaces such as T^{1,1}/Z2 and others related to Maldacena–Nuñez geometry.The work provides a bridge between AdS/CFT constructions in M-theory and well-known Sasaki-Einstein geometries, offering a rich set of candidate gravity duals for 4D N=1 superconformal field theories and highlighting future avenues in flux quantization and brane interpretations.

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.