Prof Andre Lukas

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.

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.

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.