Existence of Majorana fermions for M-branes wrapped in space and time

TL;DR

This paper demonstrates the possibility of defining Majorana spinor fields on M-branes with specific geometric identifications, ensuring consistency of supersymmetry transformations even in non-orientable configurations.

Contribution

It shows that Majorana spinors can be consistently defined on wrapped M-branes with antipodal identifications, extending the understanding of supersymmetry in non-orientable brane geometries.

Findings

Majorana spinors can be defined on antipodally identified M-branes.

Supertranslation generators transform as Majorana fermions under $Spin(10,1)$.

Results extend to p-branes with (adS)×(Sphere) throat geometries.

Abstract

We show that it is possible to define Majorana (s)pinor fields on M-branes which have been identified under the action of the antipodal map on the adS factor of the throat geometry, or which have been wrapped on two-cycles of arbitrary genus. This is an important consistency check, since it means that one may still take the generators of supertranslations in superspace to transform as Majorana fermions under the adjoint action of $Spin(10,1)$, even though the antipodally identified M2-brane is {\it not} space-orientable. We point out that similar conclusions hold for any p-branes which have the generic (adS)$~{\times}~$(Sphere) throat geometry.