I will discuss the Hopf algebraic (quantum symmetry) structures underlying certain four-dimensional finite quantum field theories which are related to the N=4 SYM theory by marginal deformations. The motivation is to understand why these theories, despite being finite (like N=4 SYM), are generically not integrable in the planar limit (unlike N=4 SYM). Apart from a better understanding of integrability, these hidden symmetries might eventually provide insight into the construction of the (still unknown) dual AdS/CFT geometries for these field theories.

This is the first lecture of a short course on non-geometric backgrounds. For more information on the course and the schedule, please visit http://www.strings.ph.qmw.ac.uk/index.htm and follow the link to the Graduate Program in String/Field Theory.

I will describe recent efforts in applying the AdS/CFT correspondence to Condensed Matter Physics. In particular, we study the charge transport properties of fields confined to a (2+1)-dimensional defect coupled to a (3+1) dimensional super-Yang-Mills theory at large-N_c and strong coupling, using AdS/CFT techniques applied to linear response theory.

TBA

The analysis of the singularities in the S-matrix of particles has shown that perturbative structure field theories can be much simpler than what Feynman diagrams tell us. In particular, there exist classes of theories whose perturbative S-matrix is completely determined by a sub-set of its singularities. At tree level this reflect with the existence of recursion relations. At loop level, there are special singularities, the leading singularities, which are believed to determine a class of theories which N=4 SYM and N=8 supergravity belongs to. I will discuss both the tree and loop level, with a particular attention on the leading singularity technique and its application to the investigation of the perturbative N=8 supergravity.

I will be reviewing the details of a novel form of the Higgs mechanism, present in the context of the Bagger-Lambert and ABJM proposals for the worldvolume description of multiple parallel M2 branes. I will also discuss some of its implications as well as describe related applications. The latter will focus on the determination of four-derivative corrections to the Bagger-Lambert A_4-theory for all values of the Chern-Simons level k

In this talk I will describe the computation of the four-point function of two weight-2 and two weight-n 1/2-BPS operators at large N and at strong 't Hooft coupling, using the supergravity approximation. I will then discuss the results in the light of the AdS/CFT correspondence.

We analyze interactions at high energies in AdS spaces, at large and small AdS curvatures. We then use the results to analyze deep inelastic scattering at small Bjorken x, using the approximate conformal invariance of QCD at high energies. Hard pomeron exchanges are resummed eikonally, restoring unitarity at large values of the phase shift in the dual AdS geometry. At weak coupling this phase is imaginary, corresponding to a black disk in AdS. In this saturated regime, cross sections exhibit geometric scaling and have a simple universal form, which we test against available experimental data for the proton structure function F2(x,Q2). We predict, in particular, the dependence of the cross section on the scaling variable (Q/Qs)2 in the deeply saturated region, where Qs is the usual saturation scale. We find agreement with current data on F2 in the kinematical region defined by Q2 between 0.5 and 10 GeV2, x less than 10E(-2), with an average 6 per cent accuracy. We conclude by discussing the relation of our approach with the commonly used dipole formalism.

The dynamics of k coincident D-branes in string theory is described effectively by U(k) Yang-Mills theory at low energy. While these configurations appear as classical solutions in matrix models, it was not clear whether it is possible to realize the k =/= 1 case as the true vacuum. We consider massive Yang-Mills-Chern-Simons matrix model and investigate the generation of higher gauge groups U(2), U(3) in this model.

I will summarise recent developments which indicate that there is a surprising duality between gluon amplitudes and Wilson loops in supersymmetric Yang-Mills theory. The motivation for the duality comes from the proposal for the strong coupling form of gluon amplitudes due to Alday and Maldacena. The evidence that the duality holds also at weak coupling comes from direct calculations of both objects and an analysis of a surprising 'dual' conformal symmetry of the gluon amplitudes which has a natural interpretation for the Wilson loops.