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

By Edward Goldstein, Sergey F. Prokushkin. 2002

213 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/43b453c0184ccec534fe455fbe2c055807a07a36

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Citations in the corpus

Four-dimensional string compactifications with D-branes, orientifolds and fluxes (2006, background): “More and also subsequent work on that subject can be found in [142, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541].”
BPS Action and Superpotential for Heterotic String Compactifications with Fluxes (2003, methodology): “8)–(2.10) is given by manifolds which are products of tori and twisted tori (included in the class of the nilmanifolds in [37]) or by torus ﬁbration of Calabi–Yau two–folds, where the ﬁber is twisted [33, 37, 42, 45, 52]. A simple instance of such spaces is given by a metric of the form ds 2= t [ds ”
Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory (2006, background): “The non-trivial twisting has an effect on the de Rham cohomology of the compactification manifold X [13,21].”
Superstrings with intrinsic torsion (2003, result): “We should also note that d = 6 geometries of the type discussed here with two flat directions are similar to those studied in [35].”
Compactifications of heterotic theory on non-Kähler complex manifolds, I (2003, methodology): “mathematical aspects of non-K¨ahler manifolds with SU(3) structure in the heterotic the- ory were given in [ 9 ].”
Compactifications of heterotic strings on non-Kähler complex manifolds II (2003, methodology): “All these solutions were shown to have zero Euler characteristics [16],[17].”
Torsional Heterotic Geometries (2009, background): “and a varying dilaton [3]. If the K3 surface is related to a quotient of a torus, these geometries are related to quotients of nilmanifolds. These geometries were shown to admit no K¨ahler metrics in [10]. There have been interesting recent constructions of torsional heterotic backgrounds using nilm”
Non-K\"ahler Calabi-Yau manifolds (2014, background): “On the other hand, much interest has been devoted to studying non-Kähler compact complex manifolds with holomorphically trivial (or more generally torsion) canonical bundle, and many examples can be found in [6, 15, 17, 20, 23, 33, 35, 36, 37, 40, 43, 53, 60, 78, 83, 86] and references therein.”
Calabi-Yau connections with torsion on toric bundles (2003, unknown): “D”
Non-Kähler Calabi-Yau manifolds (2014, background): “On the other hand, much interest has been devoted to studying non-Kähler compact complex manifolds with holomorphically trivial (or more generally torsion) canonical bundle, and many examples can be found in [6, 15, 17, 20, 23, 33, 35, 36, 37, 40, 43, 53, 60, 78, 83, 86] and references therein.”
Supersymmetric AdS(4) compactifications of IIA supergravity (2004, background): “Our starting point is the work of Goldstein and Prokushkin [50].”