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      Half-flat nilmanifolds

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          Abstract

          We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional nilmanifolds carrying an invariant half-flat structure.

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          The Geometry of Three-Forms in Six Dimensions

          Nigel Hitchin (2000)
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            Complex structures on nilpotent Lie algebras

            S.M. Salamon (2001)
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              Heterotic on Half-flat

              Andrei Micu, Andre Lukas, Sebastien Gurrieri (2004)
              We study the effective action of the heterotic string compactified on particular half-flat manifolds which arise in the context of mirror symmetry with NS-NS flux. We explicitly derive the superpotential and Kahler potential at lowest order in alpha' by a reduction of the bosonic action. The superpotential contains new terms depending on the Kahler moduli which originate from the intrinsic geometrical flux of the half-flat manifolds. A generalized Gukov formula, valid for all manifolds with SU(3) structure, is derived from the gravitino mass term. For the half-flat manifolds it leads to a superpotential in agreement with our explicit bosonic calculation. We also discuss the inclusion of gauge fields.
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                Author and article information

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                Publication date Created: 06 March 2009
                Publication date Updated: 2010-05-12
                Article
                DOI: 10.1007/s00208-010-0535-1
                ArXiV ID: 0903.1175
                SO-VID: d18b8d7c-f55d-4365-b3c5-12b014b2a06f
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                ACM classes 53C25, 53C29, 17B30
                Journal reference Mathematische Annalen, 2011, 350(1):155-168
                Comments 14 pages; v2: corrected equation in introduction; added solvable example; rearranged contents of Proposition 3 and Lemma 4; v3: corrected typos, added remark about unimodular case
                Categories math.DG

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