Supersymmetry and spin structures

TL;DR

This paper constructs specific M-theory backgrounds with varying supersymmetry depending on spin structures, focusing on AdS_4 x L with lens spaces L having cyclic fundamental groups.

Contribution

It introduces new examples of M-theory backgrounds where supersymmetry varies with spin structure choices, involving lens spaces with cyclic fundamental groups.

Findings

Supersymmetry depends on the spin structure in constructed backgrounds.

Examples involve AdS_4 x L with lens spaces L.

Fundamental group of L is cyclic of order 4k.

Abstract

We construct examples of isometric M-theory backgrounds which preserve a different amount of supersymmetry depending on the choice of spin structure. These examples are of the form AdS_4 x L, where L is a seven-dimensional lens space whose fundamental group is cyclic of order 4k.