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Abstract:

In this paper we analyze the structure of supersymmetric vacua in compactifications of the heterotic string on certain manifolds with SU(3) structure. We first study the effective theories obtained from compactifications on half-flat manifolds and show that solutions which stabilise the moduli at acceptable values are hard to find. We then derive the effective theories associated with compactification on generalized half-flat manifolds. It is shown that these effective theories are consistent with four-dimensional N ≤ 1 supergravity and that the superpotential can be obtained by a Gukov-Vafa-Witten type formula. Within these generalized models, we find consistent supersymmetric (AdS) vacua at weak gauge coupling, provided we allow for general internal gauge bundles. In simple cases we perform a counting of such vacua and find that a fraction of about 1/1000 leads to a gauge coupling consistent with gauge unification. © SISSA 2006.

Abstract:

We study the effective D=4, N=1 supergravity description of five-dimensional heterotic M theory in the presence of an M5 brane, and derive the Killing vectors and isometry group for the Kähler moduli-space metric. The group is found to be a non-semi-simple maximal parabolic subgroup of Sp(4,R), containing a nontrivial SL(2,R) factor. The underlying moduli space is then naturally realized as the group space Sp(4,R)/U(2), but equipped with a nonhomogeneous metric that is invariant only under that maximal parabolic group. This nonhomogeneous metric space can also be derived via field truncations and identifications performed on Sp(8,R)/U(4) with its standard homogeneous metric. In a companion paper we use these symmetries to derive new cosmological solutions from known ones. © 2005 The American Physical Society.