The geometry of M-branes wrapping special Lagrangian cycles

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. HUTP-05/A0021BCCUNY-HEP /05-03 hep-th/xxxxxxx *

Wrapped M5-branes leading to five dimensional 2-branes

“…This constitutes a proof of this relationship, often quoted in the literature, as well as further confirmation of both results. In addition, it provides further confirmation of the interpretation of [10] as a wrapped brane. This paper may be thought of as the sequel to an argument presented in [8] where a, much shorter, calculation has shown that a certain configuration of M-branes wrapping SLAG cycles of a Calabi-Yau with constant complex structure moduli excite only the universal hypermultiplet and result in a special case of the more general five dimensional 2-brane with full hypermultiplets discussed therein and here.…”

“…We have explicitly shown that the dimensional reduction of a M5-brane wrapping special Lagrangian 3-cycles of a Calabi-Yau manifold deforming the complex structure [10] excites only the hypermultiplets sector of ungauged five dimensional N = 2 supergravity. The D = 5 universal axion a (or its dual 3-form gauge field) vanishes and the result is a 2-brane coupled to the hypermultiplet fields [8].…”

“…In the same paper we analyzed the conditions on a more general D = 5 2-brane that couples to the full set of hypermultiplets. From the higher dimensional perspective, this is assumed to be a M5-brane wrapping SLAG cycles of a Calabi-Yau 3-fold with non-trivial complex structure moduli; the same calibrated brane configuration studied by [9] and [10]. This correspondence has been assumed without proof in most of these references.…”

“…We are only interested in the hypermultiplets, so the vector multiplets sector will be ignored. Section 3 presents the eleven dimensional SLAG-wrapped M5-brane in the form of [10] as well as the 2-brane of [8]. At the risk of confusing the reader, we had to change the notations used in the two references slightly in order to avoid using the same symbols to describe different things.…”

Geometry of wrapped M5-branes in Calabi-Yau 2-folds

“…In a recent paper [1], two of us studied M5-branes wrapping Special Lagrangian 3-cycles in Calabi-Yau three-folds. We argued that the almost complex structure of the underlying Calabi-Yau three-fold survives the wrapping.…”