L3

Recall that a difference field is a field with a distinguished automorphism. ACFA is the theory of existentially closed difference fields. I will discuss results on groups definable in models of ACFA, in particular when they are one-based and what are the consequences of one-basedness.

I will describe the recent construction of new supersymmetric compactifications of the heterotic string which yield just the spectrum of the MSSM at low energies. The starting point is the standard embedding solution on a Calabi-Yau manifold with Euler number -6 with various choices of Wilson lines, i.e., various choices of discrete holonomy for the gauge bundle. Although they yield three net generations of standard model matter, such models necessarily have a larger gauge group than the standard model, as well as exotic matter content. Families of stable bundles can be obtained by deformation of these simple solutions, the deformation playing the dual role of partially breaking the gauge group and reducing the matter content, and in this way we construct more realistic models. The moduli space breaks up into various branches depending on the initial choice of Wilson lines, and on eight of these branches we find models with exactly the standard model gauge group, three generations of quarks and leptons, two Higgs doublets, and no other massless charged states. I will also comment on why these are possibly the unique models of this type.

The AdS/CFT correspondence is a powerful tool to analyse strongly coupled quantum field

theories. Over the past few years there has been a surge of activity aimed at finding

possible applications to condensed matter systems. One focus has been to holographically

realise various kinds of phases via the construction of fascinating new classes of black

hole solutions. In this framework, I will discuss the possibility of describing finite

temperature phase transitions leading to spontaneous breaking of translational invariance of

the dual field theory at strong coupling. Along with the general setup I will also discuss

specific string/M theory embeddings of the corresponding symmetry breaking modes leading to

the description of such phases.