Calibrations, Torsion Classes and Wrapped M-Branes

TL;DR

This paper advances the classification of M-brane geometries using torsion classes and introduces new calibrations relevant for fluxed backgrounds, enhancing understanding of M-brane physics.

Contribution

It completes the classification of geometries via torsion classes and defines new energy-minimizing calibrations for fluxed M-brane backgrounds.

Findings

Classification of geometries in terms of torsion classes completed.

New calibrations relevant for flux backgrounds introduced.

Deeper insight into the physical meaning of torsion class constraints provided.

Abstract

The present work has two goals. The first is to complete the classification of geometries in terms of torsion classes of M-branes wrapping cycles of a Calabi-Yau. The second goal is to give insight into the physical meaning of the torsion class constraints. We accomplish both tasks by defining new energy minimizing calibrations in M-brane backgrounds. When fluxes are turned on, it is these calibrations that are relevant, rather than those which had previously been defined in the context of purely geometric backgrounds.