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

Abstract

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{ä}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.

References in corpus (7)

• Fivebranes, Membranes and Non-Perturbative String Theory
• Open P-Branes
• Localized intersections of M5-branes and four-dimensional superconformal field theories
• Brane Surgery
• BPS States and Minimal Surfaces
• Four-dimensional BPS-spectra via M-theory
• Calibrations and Fayyazuddin-Smith Spacetimes

Cited by in corpus (9)

• AdS spacetimes from wrapped M5 branes
• Supersymmetric wrapped membranes, AdS(2) spaces, and bubbling geometries
• AdS spacetimes from wrapped D3-branes
• Wrapped M5-branes leading to five dimensional 2-branes
• Four-dimensional SYM probes in wrapped M5-brane backgrounds
• $G_2$ holonomy metrics and wrapped D6-branes
• Central charges of wrapped M5-brane backgrounds
• Inverting geometric transitions: explicit Calabi-Yau metrics for the Maldacena-Nunez solutions
• Spacetime singularity resolution by M-theory fivebranes: calibrated geometry, Anti-de Sitter solutions and special holonomy metrics