We shall discuss aspects of how internal manifolds evolve during cosmology, paying particular attention to the regions where the manifold changes topology.

I will discuss how to use string techniques to systematically derive brane world effective actions for models with magnetized (or equivalently intersecting) D-branes. In particular, I derive the dependence on all NS-NS moduli of the kinetic terms of the chiral matter in a generic non-supersymmetric brane configurations with non-commuting open string fluxes. Near a N=1 supersymmetric point the effective action contains D and F term breaking terms which can be explicitly computed with string diagrams.

We review AdS/CFT Correspondence constructions of non-supersymmetric theories and include quarks using D7 brane probes. Such geometries provide a geometric decription of chiral symmetry breaking in the pattern of QCD. The meson masses of the theory can be computed and include a pion-like goldstone boson. Phenomenological models of QCD in this spirit surprisingly work at the 10-15 percent level. Finally we address a major concern with such models - they have strongly coupled UV physics. We use ideas from perfect lattice actions to suggest a solution and show a toy example of the method in action.

We study the quantization on the torus of the N=2 spinning particle coupled to spacetime gravity to obtain a worldline representation of the effective action of an arbitrary antisymmetric tensor field. This representation contains on top of the usual proper time a new modular parameter implementing the reduction to a single tensor field. Then we describe how to use it: (i) to calculate the first few Seeley-DeWitt coefficients for antisymmetric tensor fields of arbitrary rank in arbitrary dimensions, (ii) to derive exact duality relations, and (iii) to compute some correlation functions.

This talk will survey recently deduced features of the ten-dimensional effective action for four gravitons in type II string theories. Duality with M-theory together with supersymmetry leads to a number of nontrivial higher derivative four-graviton interactions whose non-perturbative structure is completely determined by a collection of Poisson equations on moduli space and is consistent with data provided by string perturbation theory.

I will review recent results at strong and weak coupling in N=4 SYM theory at finite temperature. I will point out that retarded correlators have a qualitatively different analytic structure in the weak a strong coupling limits and will argue that this either necessitates a phase transition in the theory or requires that we revise our current understanding of weakly coupled plasmas.

Lunin and Maldacena recently found a simple method to generate AdS_5 supergravity backgrounds dual to exactly marginal deformations of SCFTs. In the first part of the talk, we will consider extensions to AdS_4 backgrounds, concentrating on those for which dual IR 3d field theories have been proposed. In the second part, we will concentrate on the deformation of N=4 SYM in 4d and analyze a certain Penrose limit. We will be led to consider a 'modified Landau problem' and relate it to the different set of chiral operators of the deformed N=4.

The IIB supersymmetry algebra in d=10 can be extended including 10-forms. One of these is the RR 10-form, which takes part in the tadpole cancellation mechanism of the type-I string. D9-branes are electrically charged with respect to this 10-form. IIB supergravity possesses a global SL(2,R) symmetry, which the quantum theory breaks to SL(2,Z). Even if 10-forms have no dynamics, since their field-strength vanishes identically, it is possible to study their behaviour under SL(2,Z) transformations. We determine all the possible independent 10-forms as representations of SL(2,Z), and in particular we show in which multiplet the RR 10-form lies. Finally, we perform the same analysis for the IIA supersymmetry algebra, and interpret the results in terms of T-duality.

In this seminar we will look at two places where two-dimensional conformal field theory is related to the study of matrix models. The first is that a matrix model may be thought of as a statistical model on a fluctuating lattice. In the continuum limit, that is in the limit of large matrix size N, this yields a c less than 1 CFT coupled to gravity. The second relation is that the matrix model can, even before the continuum limit, be described in terms of free bosons. The free boson CFT turns out to be useful in understanding the large N behaviour of the matrix model.

KZ equations are an essential tool in the study of conformal field theories with affine algebra symmetry. They are satisfied by all correlation functions of affine primary fields. However, string theory in AdS3 forces us to consider fields which are not affine primaries. I will explain that some generalizations of the KZ equations nevertheless still hold. I will discuss the implications of this finding for the relation with Liouville theory and the operator product expansion in the H3 model.

We propose affine Toda field theories related to the non-crystallographic Coxeter groups H_2, H_3 and H_4. The classical mass spectrum, the classical three-point couplings and the one-loop corrections to the mass renormalisation are determined. The construction is carried out by means of a reduction procedure from crystallographic to non-crystallographic Coxeter groups. The embedding structure explains for various affine Toda field theories that their particles can be organised in pairs, such that their relative masses differ by the golden ratio.