The Geometry of M-Branes Wrapping Special Lagrangian Cycles

TL;DR

This paper characterizes the geometric structures arising from M5-branes wrapping special Lagrangian 3-cycles in Calabi-Yau manifolds, revealing how supersymmetry constrains the resulting real manifold's complex structures.

Contribution

It provides a classification of the geometries produced by M5-branes wrapping special Lagrangian cycles, emphasizing the roles of specific differential forms and supersymmetry constraints.

Findings

Identification of a real manifold with an almost complex structure

Role of a distinguished (1,1) form and a (3,0) form in the geometry

Supersymmetry imposes specific constraints on these structures

Abstract

We characterize the geometry produced by M5-branes wrapping a Special Lagrangian 3-cycle in a Calabi-Yau 3-fold. The presence of the brane replaces the the Calabi-Yau by a real manifold with an almost complex structure. We show that, in this classification, a distinguished (1,1) form as well as a globally defined (3,0) form play an important role. The requirements of supersymmetry preservation impose constraints on these structures which can be used to classify the background.