Supersymmetric AdS Backgrounds in String and M-theory

TL;DR

Gauntlett, Martelli, Sparks, and Waldram develop a G-structure framework for classifying supersymmetric flux backgrounds and extract general $ ext{AdS}_5$ conditions in M-theory, producing new compact $ ext{AdS}_5 imes X$ solutions with complex $X$ that fiber over KE bases. They further construct an infinite family of Sasaki--Einstein manifolds in type IIB from KE bases, including regular, quasi-regular, and irregular examples, and demonstrate a product-base generalization; these yield new AdS$_5$ duals with varied R-charges and central charges. The results expand the landscape of explicit AdS backgrounds and SE manifolds, with broad implications for AdS/CFT and flux-compactification techniques, and they provide systematic tools for generating further SUSY solutions via $G$-structures and calibrated brane configurations. The work highlights the deep connections between intrinsic torsion, generalized calibrations, and brane physics in constructing and interpreting supersymmetric backgrounds.

Abstract

We first present a short review of general supersymmetric compactifications in string and M-theory using the language of G-structures and intrinsic torsion. We then summarize recent work on the generic conditions for supersymmetric AdS_5 backgrounds in M-theory and the construction of classes of new solutions. Turning to AdS_5 compactifications in type IIB, we summarize the construction of an infinite class of new Sasaki-Einstein manifolds in dimension 2k+3 given a positive curvature Kahler-Einstein base manifold in dimension 2k. For k=1 these describe new supergravity duals for N=1 superconformal field theories with both rational and irrational R-charges and central charge. We also present a generalization of this construction, that has not appeared elsewhere in the literature, to the case where the base is a product of Kahler-Einstein manifolds.