We discuss how the duality group G controls the higher derivative corrections that arise in the effective action of M-theory compactified on a torus. In particular we show that the perturbative contributions always involve the weights of G and that this is a consequence of the appearance of automorphic forms of G in the complete quantum effective action.

String perturbation theory in the presence of D-branes is usually described in terms of conformal field theory (CFT) on worldsheets with boundaries. In this formalism, closed string scattering amplitudes in the presence of static Dp-branes exhibit infrared divergences for p=0 and p=1, so the worldsheet CFT description breaks down. For p=0, it is known that these divergences are due to D0-brane recoil. A systematic framework to take recoil into account is the worldline formalism, where fixed boundary conditions are replaced by dynamical D0-brane worldlines. In this formalism, the divergences that plague the worldsheet CFT are automatically cancelled in a non-trivial way. The amplitudes derived in the worldline formalism can be reproduced by deforming the CFT with a specific bilocal recoil operator. For p=1, the divergences are due to local recoil of D1-branes, which (classically) end up displaced a finite distance from their original position. The quantum version of this phenomenon can be viewed as a simple geometric manifestation of the absence of spontaneous symmetry breaking in 1+1 dimensions. Through a Dirac-Born-Infeld analysis, it is possible to resum these divergences in a way that yields finite, momentum-conserving amplitudes.

The Kahler metric for chiral matter fields plays a crucial role in the computation of soft supersymmetry breaking terms in string compactifications. Due to its non-holomorphic nature, this is difficult to compute in Calabi-Yau backgrounds. I describe techniques that allow the modular weights of the Kahler metric to be computed in IIB string compactifications. This is done by relating the modular dependence of the Kahler metric to that of the physical Yukawa couplings. I briefly discuss the applications to soft terms and neutrino masses.

In this work we define a new limiting procedure that extends the usual thermodynamics treatment of Black Hole physics, to the supersymmetric regime. This procedure is inspired on equivalent statistical mechanics derivations in the dual CFT theory, where the BPS partition function at zero temperature is obtained by a double scaling limit of temperature and the relevant chemical potentials. In supergravity, the resulting partition function depends on emergent generalized chemical potentials conjugated to the different conserved charges of the BPS solitons. With this new approach, studies on stability and phase transitions of supersymmetric solutions are presented. We find stable and unstable regimes with first order phase transitions, as suggested by previous studies on free supersymmetric Yang Mills theory.

In these lectures, I will introduce the concept of integrability and study its realisation in the context of gauge theory and string theory. In particular, I plan to review recent progress in computing the spectrum of operator dimensions in N=4 supersymmetric Yang-Mills theory and the dual problem of determining the spectrum of string theory on AdS5 x S5.

Negative curvature Euclidean (Hyperbolic) spaces have already been used in literature as part of eleven dimensional supergravity solutions. In particular it has been shown that they naturally appear when building expanding cosmological models. In this talk I will present M-theory solutions written as direct products of maximally symmetric spaces with hyperbolic components. These backgrounds break supersymmetry because of global effects but are still stable with respect to small scalar perturbations. They appear as near-horizon geometries for wrapped M5-branes, thus allowing for an intuitive interpretation of their stability.

In these lectures, I will introduce the concept of integrability and study its realisation in the context of gauge theory and string theory. In particular, I plan to review recent progress in computing the spectrum of operator dimensions in N=4 supersymmetric Yang-Mills theory and the dual problem of determining the spectrum of string theory on AdS5 x S5.

I will begin with basic review on the integrabilities in AdS/CFT correspondence, and move on discussing the role of scattering matrices in gauge and string thoeries. I will then explain the formation of magnon boundststates in gauge theory and their corresponding classical string solution. The scattering of magnon boundstates and their classifications will also be discussed in this seminar. I will also mention some work in progress.

In these lectures, I will introduce the concept of integrability and study its realisation in the context of gauge theory and string theory. In particular, I plan to review recent progress in computing the spectrum of operator dimensions in N=4 supersymmetric Yang-Mills theory and the dual problem of determining the spectrum of string theory on AdS5 x S5.

We will discuss the one-loop anomalous dimensions of Super Yang-Mills operators dual to open strings ending on AdS giant gravitons (AGG) and describe the spin chain description of gauge theory operators. A semi-classical analysis of the Hamiltonian describing the anomalous dimensions of AGG operators will allow us to give a geometrical (stringy) interpretation for the gauge theory parameters. This same analysis will also show evidence for the existence of continuous bands in the Hamiltonian spectrum.

In these lectures, I will introduce the concept of integrability and study its realisation in the context of gauge theory and string theory. In particular, I plan to review recent progress in computing the spectrum of operator dimensions in N=4 supersymmetric Yang-Mills theory and the dual problem of determining the spectrum of string theory on AdS5 x S5.

In these lectures, I will introduce the concept of integrability and study its realisation in the context of gauge theory and string theory. In particular, I plan to review recent progress in computing the spectrum of operator dimensions in N=4 supersymmetric Yang-Mills theory and the dual problem of determining the spectrum of string theory on AdS5 x S5.

This the first of a series of lectures in which I will introduce the concept of integrability and study its realisation in the context of gauge theory and string theory. In particular, I plan to review recent progress in computing the spectrum of operator dimensions in N=4 supersymmetric Yang-Mills theory and the dual problem of determining the spectrum of string theory on AdS5 x S5.

I will present a modification of the Berkovits twistor string model which gives Einstein supergravity coupled to Yang-Mills, and has a limit in which the gravity modes can be decoupled to give pure gauge theory amplitudes. I will start by reviewing a number of relevant aspects of twistor theory, including special features associated with different space-time signatures, supertwistor space, the Penrose transform, the infinity twistor and Penrose's non-linear graviton construction. I will then review the Witten and Berkovits twistor strings, with emphasis on the latter. The world-sheet formulation of the Berkovits model involves so-called beta-gamma systems, I will describe the symmetries of such systems and their gauging, and explain how the analysis can be applied to the construction of a family of new gauged Berkovits twistor strings which are free from world-sheet anomalies. I will also describe the corresponding spectra in space-time, and show that they give Einstein supergravities instead of the higher derivative conformal supergravities arising in the original twistor string models. The new theories include one with the spectrum of N = 8 supergravity, two theories with the spectrum of N = 4 supergravity coupled to N = 4 Yang-Mills, a family of N greater than 0 models with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills, and a non-supersymmetric string with the spectrum of self-dual gravity coupled to self-dual Yang-Mills and a scalar. Time permitting, I will discuss what is known about the interactions.