Heterotic String Compactification and New Vector Bundles

Abstract

We propose a construction of Kähler and non-Kähler Calabi-Yau manifolds by branched double covers of twistor spaces. In this construction we use the twistor spaces of four-manifolds with self-dual conformal structures, with the examples of connected sum of n P 2 s. We also construct K3-fibered Calabi-Yau manifolds from the branched double covers of the blow-ups of the twistor spaces. These manifolds can be used in heterotic string compactifications to four dimensions. We also construct stable and polystable vector bundles. Some classes of these vector bundles can give rise to supersymmetric grand unified models with three generations of quarks and leptons in four dimensions.

Holomorphic string algebroids

“…× h k , we obtain a Courant extension of P , and hence a string algebroid, by applying Proposition 2.4. Explicit constructions of such bundles for X a compact Calabi-Yau threefold with k = 1, V 0 = T X and V 1 not isomorphic to V 0 can be found in [2,11,21,19,25] and references therein.…”

Higher dimensional generalizations of twistor spaces

“…Also all such maps are the branch covering of P 1 . This case was analysed by [16], and see related discussions of g = 3 case [35] and g = 1 case [22].…”

“…For a non-Kähler balanced manifold, its Hermitian form ω is not closed, however, ω p−1 is closed, where p is the complex dimension of the manifold. Under appropriate blowing-downs or contractions of curves, some classes of non-Kähler balanced manifolds can become Kähler and have projective models in algebraic geometry (see for example [43,32,35]).…”

“…For the cases n ≥ 2, the twistor spaces Tw(nP 2 ) are non-Kähler manifolds (see [32,44,31]). The branched double covers of the twistor spaces were analyzed in [35,22], in which by choosing appropriate branch divisors, the branched double covers can give rise to non-Kähler Calabi-Yau manifolds, with trivial canonical bundle. They provide interesting examples of non-Kähler Calabi-Yau manifolds (see for example [56,54,35]).…”

“…They provide interesting examples of non-Kähler Calabi-Yau manifolds (see for example [56,54,35]). We can also construct various vector bundles on them [35]. 1 Another class of manifolds whose twistor spaces are very interesting are the hyper-Kähler and hypercomplex manifolds.…”