The Atiyah class and complex structure stabilization in heterotic Calabi-Yau compactifications
Journal of High Energy Physics 2011:10 (2011)
Abstract:
Holomorphic gauge fields in N = 1 supersymmetric heterotic compactifications can constrain the complex structure moduli of a Calabi-Yau manifold. In this paper, the tools necessary to use holomorphic bundles as a mechanism for moduli stabilization are systematically developed. We review the requisite deformation theory - including the Atiyah class, which determines the deformations of the complex structure for which the gauge bundle becomes non-holomorphic and, hence, non-supersymmetric. In addition, two equivalent approaches to this mechanism of moduli stabilization are presented. The first is an efficient computational algorithm for determining the supersymmetric moduli space, while the second is an F-term potential in the four-dimensional theory associated with vector bundle holomorphy. These three methods are proven to be rigorously equivalent. We present explicit examples in which large numbers of complex structure moduli are stabilized. Finally, higher-order corrections to the moduli space are discussed. © 2011 SISSA.Two hundred heterotic standard models on smooth Calabi-Yau threefolds
Physical Review D - Particles, Fields, Gravitation and Cosmology 84:10 (2011)
Abstract:
We construct heterotic standard models by compactifying on smooth Calabi-Yau three-folds in the presence of purely Abelian internal gauge fields. A systematic search over complete intersection Calabi-Yau manifolds with less than six Kähler parameters leads to over 200 such models which we present. Each of these models has precisely the matter spectrum of the minimal supersymmetric standard model, at least one pair of Higgs doublets, the standard model gauge group, and no exotics. For about 100 of these models there are four additional U(1) symmetries which are Green-Schwarz anomalous and, hence, massive. In the remaining cases, three U(1) symmetries are anomalous, while the fourth, massless one can be spontaneously broken by singlet vacuum expectation values. The presence of additional global U(1) symmetries, together with the possibility of switching on singlet vacuum expectation values, leads to a rich phenomenology which is illustrated for a particular example. Our database of standard models, which can be further enlarged by simply extending the computer-based search, allows for a detailed and systematic phenomenological analysis of string standard models, covering issues such as the structure of Yukawa couplings, R-parity violation, proton stability, and neutrino masses. © 2011 American Physical Society.G-structures and domain walls in heterotic theories
Journal of High Energy Physics 2011:1 (2011)
Abstract:
We consider heterotic string solutions based on a warped product of a fourdimensional domain wall and a six-dimensional internal manifold, preserving two supercharges. The constraints on the internal manifolds with SU(3) structure are derived. They are found to be generalized half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that previous heterotic compactifications on half-flat mirror manifolds are based on this class of solutions. © SISSA 2011.Stabilizing all geometric moduli in heterotic Calabi-Yau vacua
Physical Review D - Particles, Fields, Gravitation and Cosmology 83:10 (2011)
Abstract:
We propose a scenario to stabilize all geometric moduli-that is, the complex structure, Kähler moduli, and the dilaton-in smooth heterotic Calabi-Yau compactifications without Neveu-Schwarz three-form flux. This is accomplished using the gauge bundle required in any heterotic compactification, whose perturbative effects on the moduli are combined with nonperturbative corrections. We argue that, for appropriate gauge bundles, all complex structure and a large number of other moduli can be perturbatively stabilized-in the most restrictive case, leaving only one combination of Kähler moduli and the dilaton as a flat direction. At this stage, the remaining moduli space consists of Minkowski vacua. That is, the perturbative superpotential vanishes in the vacuum without the necessity to fine-tune flux. Finally, we incorporate nonperturbative effects such as gaugino condensation and/or instantons. These are strongly constrained by the anomalous U(1) symmetries, which arise from the required bundle constructions. We present a specific example, with a consistent choice of nonperturbative effects, where all remaining flat directions are stabilized in an anti-de Sitter vacuum. © 2011 American Physical Society.Stabilizing the complex structure in heterotic Calabi-Yau vacua
Journal of High Energy Physics 2011:2 (2011)