N=4 super Yang-Mills theory has a remarkable feature of being integrable. This discovery has made it possible to achieve strong evidence for the AdS/CFT duality. But what about its siblings: marginal deformations of N=4 SYM that preserve conformal symmetry. In this case much less is known about the conjectured supergravity dual. In particular, the Leigh-Strassler deformations are of this kind, which are only integrable for some special values of the deformation parameters, or in some restricted subsectors. In order to gain more insight into the theory, one would like to understand the symmetries of the theory better. We know that the symmetries of integrable systems can be described by Hopf algebras. Here we would like to show that a Hopf algebra structure actually emerges for the generic Leigh-Strassler deformation.

In recent years there have been quantum leaps in the development of calculational technology for field theory amplitudes, partly captured by the buzzwords in the title of this talk. Interestingly, most of these developments are rooted within field theory ideas of the sixties which centered around the 'analytic S-matrix'. This line of thought led to the birth of string theory with Veneziano's amplitude. It therefore seems a natural question if these recent field theory ideas can be found within the frame-work of string theory amplitudes. On the basis of three examples, I will argue that this is not only natural but profitable.

We construct new exact solutions of pure gravity in five dimensions representing black rings in Taub-NUT spaces, both at zero and at non-zero temperature. We use these solutions to study properties of the D0-D6 system in the supergravity approximation. In particular we compute the interaction energy between D0 and D6 branes, analyze equilibrium configurations and their stability.

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by writing the quaternionic geometry on the hypermultiplet moduli space in terms of twistor geometry. Using this twistor space approach, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions.

In this talk we will consider dynamics with infinitely many time derivatives, such equations follow directly from string field theory and have many interesting properties. First we will review results for the case of Minkowski background and then consider coupling to nontrivial background, in particular, to Friedmann-Robertson-Walker metric. New methods for solving corresponding nonlocal Friedmann equations will be presented and resulting solutions in the view of cosmological applications will be discussed.

A brane tiling is a bicolored graph on an oriented real 2torus, which conjecturally describes both the derived category of coherent sheaves on a 2dimensional toric Fano stack and the derived category of the directed Fukaya category of the mirror. When the toric Fano stack is the projective plane, the corresponding brane tiling divides the torus into three hexagons. In the talk, based on a joint work in progress with Masahiro Futaki, I will describe the analogue of brane tiling for the projective space, which divides the real 3torus into four truncated octahedra, and explain how it helps to study a torus-equivariant version of homological mirror symmetry.

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.

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.