Timelike Killing spinors in seven dimensions

TL;DR

This work develops a G-structure approach to seven-dimensional minimal and $SU(2)$ gauged supergravity, showing that a timelike Killing spinor induces an $SU(3)$ structure on a 6D base and deriving necessary and sufficient conditions for such supersymmetry; using this framework, the authors construct broad classes of explicit solutions, including Gödel-like backgrounds with closed timelike curves and various AdS-type vacua. The methodology yields a unified, constructive ansatz that fixes much of the bosonic content via the $SU(3)$ structure while leaving controlled torsion components, enabling systematic generation of new solutions across Calabi–Yau, semi-Kähler, and Hermitian bases in the minimal theory, and abelian gauged cases with $U(1)$ truncations in the gauged theory. A notable finding is the generic presence of CTCs in timelike supersymmetric solutions, motivating further exploration of quotienting, universal covers, or chronology-protection mechanisms; the paper also outlines directions for fully non-abelian Yang–Mills solutions and the null (lightlike) class. Overall, the results advance systematic construction and classification of timelike SUSY backgrounds in seven dimensions and illuminate their lift to higher-dimensional string/M-theory vacua.

Abstract

We employ the G-structure formalism to study supersymmetric solutions of minimal and SU(2) gauged supergravities in seven dimensions admitting Killing spinors with associated timelike Killing vector. The most general such Killing spinor defines an SU(3) structure. We deduce necessary and sufficient conditions for the existence of a timelike Killing spinor on the bosonic fields of the theories, and find that such configurations generically preserve one out of sixteen supersymmetries. Using our general supersymmetric ansatz we obtain numerous new solutions, including squashed or deformed AdS solutions of the gauged theory, and a large class of Godel-like solutions with closed timelike curves.