Prof Andre Lukas

Abstract:

We construct M theory on the orbifold C2/ZN by coupling 11-dimensional supergravity to a seven-dimensional Yang-Mills theory located on the orbifold fixed plane. It is shown that the resulting action is supersymmetric to leading nontrivial order in the 11-dimensional Newton constant. This action provides the starting point for a reduction of M theory on G2 spaces with codimension four singularities. © 2006 The American Physical Society.

Abstract:

We derive a set of exact cosmological solutions to the D=4, N=1 supergravity description of heterotic M theory. Having identified a new and exact SU(3) Toda model solution, we then apply symmetry transformations to both this solution and to a previously known SU(2) Toda model, in order to derive two further sets of new cosmological solutions. In the symmetry-transformed SU(3) Toda case we find an unusual bouncing motion for the M5 brane, such that this brane can be made to reverse direction part way through its evolution. This bounce occurs purely through the interaction of nonstandard kinetic terms, as there are no explicit potentials in the action. We also present a perturbation calculation which demonstrates that, in a simple static limit, heterotic M theory possesses a scale-invariant isocurvature mode. This mode persists in certain asymptotic limits of all the solutions we have derived, including the bouncing solution. © 2006 The American Physical Society.

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.