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Five-brane superpotentials, blow-up geometries and SU(3) structure manifolds

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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 \( \mathcal{N} = 1 \) 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-Kähler SU(3) structure and an identification of the three-form flux.

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  1. Bethe Center for Theoretical Physics, Universität Bonn, Nussallee 12, 53115, Bonn, Germany

    Thomas W. Grimm, Albrecht Klemm & Denis Klevers

  2. Max Planck Institute for Physics, Föhringer Ring 6, 80805, Munich, Germany

    Thomas W. Grimm

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  1. Thomas W. Grimm
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ArXiv ePrint: 1011.6375

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Grimm, T.W., Klemm, A. & Klevers, D. Five-brane superpotentials, blow-up geometries and SU(3) structure manifolds. J. High Energ. Phys. 2011, 113 (2011). https://doi.org/10.1007/JHEP05(2011)113

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