Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds
arXiv:1011.6375 · doi:10.1007/JHEP05(2011)113
Abstract
We investigate the dynamics of space-time filling five-branes wrapped on curves in heterotic and orientifold Calabi-Yau compactifications. We first study the leading N=1 scalar potential on the infinite deformation space of the brane-curve around a supersymmetric configuration. The higher order potential is also determined by a brane superpotential which we compute for a subset of light deformations. We argue that these deformations map to new complex structure deformations of a non-Calabi-Yau manifold which is obtained by blowing up the brane-curve into a four-cycle and by replacing the brane by background fluxes. This translates the original brane-bulk system into a unifying geometrical formulation. Using this blow-up geometry we compute the complete set of open-closed Picard-Fuchs differential equations and identify the brane superpotential at special points in the field space for five-branes in toric Calabi-Yau hypersurfaces. This has an interpretation in open mirror symmetry and enables us to list compact disk instanton invariants. As a first step towards promoting the blow-up geometry to a supersymmetric heterotic background we propose a non-Kaehler SU(3) structure and an identification of the three-form flux.
95 pages, 4 figures; v2: Minor corrections, references updated
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Cited by in corpus (14)
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- The Atiyah Class and Complex Structure Stabilization in Heterotic Calabi-Yau Compactifications
- The effective action of D6-branes in N=1 type IIA orientifolds
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