The total cross section for the scattering of a quark anti-quark dipole on a large nucleus at high energy is calculated. The system is studied within the framework of a strongly coupled N = 4 super Yang-Mills theory and the problem is solved using the AdS/CFT correspondence. The nucleus is modeled by a metric of a shock wave in AdS5. The expectation value of the Wilson loop (the dipole) is calculated by finding the extrema of the Nambu-Goto action for an open string attached to the quark and antiquark lines of the loop in the background of an AdS5 shock wave. Two physically meaningful extremal string configurations are found. For both solutions, the forward scattering amplitude N for the quark dipolenucleus scattering is found and is being investigated. The results are analyzed and compared with those in the literature. In particular for both solutions the saturation scale Qs (i.e. the scale where the partons densities inside the nucleus reach their maximum values) at high enough energy, becomes energy independent. In addition, the pomeron intercept that corresponds to a single graviton exchange is calculated and conjectured to be equal to aP =1.5.

There has been much recent interest in the proposed duality between superstrings in the curved geometry AdS_4 x P3 and three dimensional N=6 supersymmetric Chern-Simons theory -- a new, concrete, example of the holographic AdS/CFT correspondence. This dual pair has additionally been conjectured to be an integrable system in the planar limit. In this talk I will discuss several classes of classical strings moving in this background, and their quantum corrections, as tools to probe the duality and to test the conjectured integrable structure.

A specific configuration of the bosonic string is discussed, in time-dependent backgrounds, which satisfies Weyl invariance to all orders in the alpha'-expansion. Conformal invariance, valid in any space time dimension, is based on the homogeneity (in time) of the Weyl-beta functions which, using field redefinitions, can be made to vanish.

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.

Toric varieties have proved to be a fabulous testing ground for questions in algebraic geometry and string theory for many years. I will describe work in progress with Greg Smith that lays the foundation for a noncommutative analogue. As applications, I will provide a multigraded version of Beilinson's theorem on the derived category of projective space and I will propose a concrete link to dimer models.

I start by giving a brief introduction to the duality between string theory and gauge theories. I will underscore the dictionary between geometrical data on the string side, and dynamical effects on the gauge theory side. Different kinds of fractional branes lead to different IR dynamics, such as confinement, Coulomb branches, and runaway or metastable supersymmetry breaking. I then review a model, D3-branes on the orbifold of the conifold, that displays all of the above behaviors. Of particular interest is the case when different fractional branes are present at the same time, leading to a rich dynamical interplay.

A precise method for relating quite general kinds of metric 3-algebras with metric Lie algebras and their unitary representations will be described. Several special cases of this construction will be highlighted, that apply to certain types of superconformal field theories dual to M2-brane configurations. Recognition of M-theoretic properties in terms of Lie-algebraic data will be noted in passing. Some remarks will be made on the general structure of metric Lie 3-algebras, which describe maximally supersymmetric Bagger-Lambert theories.

We consider the large spin expansions of anomalous dimensions for twist operators in N=4 SYM and their AdS counterpart in terms of energies of some classical string configurations. Evidence is given, both at weak and strong coupling in perturbation theory, that they respect a generalization of the property known in QCD as Gribov-Lipatov reciprocity.

As parameters in quantum mechanics are slowly varied, states undergo a non-Abelian holonomy known as Berry phase. I will review the ideas behind the Berry phase and explain how supersymmetry imposes restrictions on the holonomy. The associated non-Abelian gauge connections must obey certain first order equations which are related to the self-dual Yang-Mills equations, specifically the Hitchin equations, tt star equations, and Bogomolnyi equations. I will end by showing how one can build a BPS 't Hooft-Polyakov monopole in the lab.

I will examine the string dual of the recently constructed N = 6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). In particular I will focus on the SU(2)X SU(2) sector. I will derive the full magnon dispersion relation and compare it to recently found results for ABJM theory at weak coupling. Then I will consider finite-size corrections to the energy of string states in the R X S2 X S2 subspace of AdS4 X CP3 with an angular momentum J on CP3 being large, using two different approaches. I will compare the results with the recently proposed all-loop Bethe ansatz of Gromov and Vieira.

We will discuss the missing pieces in the understanding of the effective field theory description of string creation, the S-dual of the Hanany-Witten effect, both in the open and closed string picture. We explain the origin of a crucial bare Chern-Simons term, that used to be added in by hand for consistency. Finally we summarize the remaining unsettled issues, concerning the need to modify the DBI action and the interpretation of the bare term in M-theory.

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 result in the light of the AdS/CFT correspondence.

I am going to review, in the context of gauge theories, the anomalous dimension of twist two operators, the cusp anomaly of Wilson loops and how they relate through AdS/CFT to rotating strings in AdS space. Then I'm going to describe in more detail the spiky strings and their properties for large spin which allows us to obtain a relation between the anomalous dimension of twist two operators and the pp-wave anomaly, an anomaly we find when N=4 SYM theory is put in a pp-wave background. Finally I'm going to consider various new open string solutions describing Wilson loops in a pp-wave and in flat space. Based on 0802.2039 and 0804.3438.

First of two lectures. For details, please consult the webpage www.ma.ic.ac.uk (slash) (tilde) rpwt (slash) LMS.html (sorry, triangle server does not allow special characters)