Killing spinors of some supergravity solutions

TL;DR

This paper explicitly computes Killing spinors for various ten-dimensional supergravity solutions, including conifold-based backgrounds and non-commutative deformations, enhancing understanding of supersymmetry in these geometries.

Contribution

It provides explicit formulas for Killing spinors in several important supergravity backgrounds, including singular, resolved, and deformed conifolds, and non-commutative geometries.

Findings

Explicit Killing spinors for conifold solutions

Killing spinors for Klebanov-Witten and Klebanov-Tseytlin backgrounds

Killing spinors for the non-commutative Maldacena-Núñez geometry

Abstract

We compute explicitly the Killing spinors of some ten dimensional supergravity solutions. We begin with a 10d metric of the form $\RR^{1,3}\times{\cal Y}_6$, where ${\cal Y}_6$ is either the singular conifold or any of its resolutions. Then, we move on to the Klebanov-Witten and Klebanov-Tseytlin backgrounds, both constructed over the singular conifold; and we also study the Klebanov-Strassler solution, built over the deformed conifold. Finally, we determine the form of the Killing spinors for the non-commutative deformation of the Maldacena-N\'u\~nez geometry.