The geometry of wrapped M5-branes in Calabi-Yau 2-folds

Details The geometry of wrapped M5-branes in Calabi-Yau 2-folds The geometry of wrapped M5-branes in Calabi-Yau 2-folds

2005-09-01

arxiv.org/abs/hep-th/0509018v1

Phys.Rev.D73:126004,2006

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1103/PhysRevD.73.126004

We study the geometry of M5-branes wrapping a 2-cycle which is Special Lagrangian with respect to a specific complex structure in a Calabi-Yau two-fold. Using methods recently applied to the three-fold case, we are again able find a characterization of the geometry, in terms of a non-integrable almost complex structure and a (2,0) form. This time, however, due to the hyper-K{\"a}hler nature of the underlying 2-fold we also have the freedom of choosing a different almost complex structure with respect to which the wrapped 2-cycle is holomorphic. We show that this latter almost complex structure is integrable. We then relate our geometry to previously found geometries of M5-branes wrapping holomophic cycles and go further to prove some previously unknown results for M5-branes on holomorphic cycles.

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