Sasakian manifolds and M-theory

TL;DR

This paper explores the relationship between Einstein Sasakian manifolds and Killing spinors, extending to $ta$-Einstein Sasakian manifolds in various settings, and introduces new supersymmetric M-theory backgrounds based on these geometries.

Contribution

It generalizes the link between Einstein Sasakian manifolds and Killing spinors to $ta$-Einstein Sasakian manifolds and proposes a new class of supersymmetric M-theory backgrounds.

Findings

Characterization of $ta$-Einstein Sasakian manifolds via generalized Killing spinors

Definition of supersymmetric M-theory backgrounds on these geometries

Discovery of a new class of supersymmetric M-theory backgrounds

Abstract

We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of $\eta$-Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterising them in terms of generalised Killing spinors. We propose a definition of supersymmetric M-theory backgrounds on such a geometry and find a new class of such backgrounds, extending previous work of Haupt, Lukas and Stelle.