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Geometric Model for Complex Non-Kähler Manifolds with SU (3) Structure

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Abstract

For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consider the case of M being a Calabi-Yau 2-fold. We show that for such M, there is a subclass of the 3-folds that we construct, which has natural families of non-Kähler SU(3)-structures satisfying the conditions for supersymmetry in the heterotic string theory compactified on the 3-folds. We present examples in the aforementioned subclass with M being a K3-surface and a 4-torus.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Edward Goldstein

  2. Department of Physics, Stanford University, Stanford, CA, 94305, USA

    Sergey Prokushkin

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  1. Edward Goldstein
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  2. Sergey Prokushkin
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Correspondence to Edward Goldstein.

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Communicated by N. Nekrasov

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Goldstein, E., Prokushkin, S. Geometric Model for Complex Non-Kähler Manifolds with SU (3) Structure. Commun. Math. Phys. 251, 65–78 (2004). https://doi.org/10.1007/s00220-004-1167-7

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