Refining G-structure classifications

TL;DR

This paper introduces a systematic formalism using G-structure language to classify and analyze supersymmetric configurations in supergravity, providing a structured approach to identify conditions for Killing spinors and solutions.

Contribution

The paper develops an iterative G-structure based method to determine conditions for Killing spinors, applied to gauged SU(2) supergravity in seven dimensions, advancing classification techniques.

Findings

Identified possible isotropy groups for Killing spinors.

Derived constraints for additional Killing spinors.

Constructed numerous solutions in gauged supergravity.

Abstract

Using G-structure language, a systematic, iterative formalism for computing neccessary and sufficient conditions for the existence of N arbitrary linearly independent Killing spinors is presented. The key organisational tool is the common isotropy group of the Killing spinors. The formalism is illustrated for configurations in gauged SU(2) supergravity in seven dimensions admitting at least one null Killing spinor, and the possible isotropy groups are shown to be $(SU(2)\ltimes\mathbb{R}^4)\times\mathbb{R}$, SU(2), $\mathbb{R}^5$, or the identity. The constraints associated with the existence of certain additional Killing spinors are computed, and used to derive numerous solutions. A discussion of the relevance of the formalism to the complete classification of all supersymmetric configurations in d=11 is given.