The Geometry of M-Branes Wrapping Special Lagrangian Cycles

We look at an M5-brane wrapping a Special Lagrangian 3-cycle in a Calabi-Yau 3-fold and study the geometry that arises when the backreaction of this brane is taken into account. Not surprisingly, the background does not remain complex. However an almost complex structure survives, (in terms of which we can define the analogue of the Kahler form), as does a globally defined (3,0) form. The requirements of supersymmetry preservation impose certain constraints on these structures which can be used to classify the background. HUTP-05/A0021 hep-th/xxxxxxx email: [email protected] email: [email protected]