A complete intersection Calabi-Yau manifold Y, will be presented. This manifold that has Euler number -72 and admits free actions by two groups of automorphisms of order 12. These are the cyclic group Z12 and the non-Abelian dicyclic group Dic3. The quotient manifolds have chi=-6 and Hodge numbers (h11, h21) = (1,4). With the standard embedding of the spin connection in the gauge group, Y gives rise to an E6 gauge theory with 3 chiral generations of particles. The gauge group may be broken further by means of the Hosotani mechanism combined with continuous deformation of the background gauge field. For the non-Abelian quotient we obtain a model with 3 generations with the gauge group broken to that of the standard model. Moreover there is a limit in which the quotients develop 3 conifold points. These singularities may be resolved simultaneously to give another manifold with (h11, h21) = (2,2) that lies right at the tip of the distribution of Calabi-Yau manifolds. This strongly suggests that there is a heterotic vacuum for this manifold that derives from the 3 generation model on the quotient of Y. The manifold Y may also be realised as a hypersurface in the toric variety. The symmetry group does not act torically, nevertheless we are able to identify the mirror of the quotient manifold by adapting the construction of Batyrev.

After a quick review of transplanckian-energy string collisions I will focus on a recent S-matrix approach to gravitational scattering and on its surprisingly good consistency with known results in classical gravitational collapse. A number of yet unresolved issues will also be presented.

An introductory review of the foundations of the Attractor Mechanism in extremal black holes in d=4 supergravity theories will be given. The issues of the classification of black hole attractors, of their stability and of the definition of an effective potential in the scalar manifold will be addressed. Finally, some recent developments will be shortly considered, such as the charge orbits and the moduli spaces of attractor solutions in N=2 and extended supergravities, and the generalization of the Attractor Mechanism to intersecting configurations of black branes in higher dimensions.

A large family of interacting conformal field theories in four dimensions with N=2 supersymmetry was recently constructed by Gaiotto. Each gauge theory is associated to a Riemann surface with certain allowed singularities. In fact, it was proposed by Alday, Gaiotto and Tachikawa that the partition function of these theories (based on SU(2) gauge groups) is equal to correlation function in Liouville theory with central charge c=25. After reviewing these constructions I will turn to a detailed exploration of S-duality using loop operators: Wilson, 't Hooft and dyonic. I will explain the classification and evaluation of arbitrary loops in arbitrary theories and show how they transform into each-other under S-duality.

The dynamics of vortices and quasiparticles in holographic realizations of 2+1 dimensional strongly interacting systems are studied in the presence of magnetic field. The first part of the seminar will discuss holographic superconductors and the second part will discuss holographic realizations of Fermi surfaces.

Quantum phase transitions imply certain scaling relations among space and time. A subclass of quantum critical systems is in fact invariant under relativstic conformal symmetries. Such theories have recently been studied as a new class of duals in AdS/CFT. I will describe how one can exactly embed so-called holographic superconductors in M-theory and how this embedding has already lead to new insights about the low-temperature behaviour of holgraphic superconductors with an underlying quantum critical point.

Sigma models endowed with target space supersymmetry have an array of peculiar properties and important applications. A new method is presented, whereby the computation of certain correlation functions in these theories is drastically simplified. In particular, this allows for the identification of new families of conformally invariant 2d sigma models.

Gauge-gravity duality is an extremely useful tool for studying strongly-coupled gauge theories, and has many applications to real-world systems, such as the quark-gluon plasma and quantum critical points. Most gauge-gravity dualities involve a gauge theory with fields only in the adjoint representation of the gauge group. In many strongly-coupled systems, however, such as the quark-gluon plamsa, fields in the fundamental representation of the gauge group, 'flavor fields', are crucially important. For (3+1)-dimensional gauge theories with gravity duals (AdS5/CFT4), the supergravity description of flavor fields is well-understood: flavor fields appear in supergravity as probe D-branes in AdS5. The story for (2+1)-dimensional gauge theories (AdS4/CFT3) is much less developed. Indeed, for supergravity on AdS4 x S7, the dual (2+1)-dimensional field theory (without flavor) was only recently discovered. In this talk I will describe how to add flavor to this theory. In particular, I will present a general recipe to determine the field theory, and in particular the couplings of the flavor fields, given a probe D-brane in AdS4.

In this talk, I will discuss a new family of supersymmetric Wilson loop operators in N=4 SYM. These operators can be defined for any loop on a three-sphere in space-time and generically preserve two super-conformal charges. On the string side, via AdS/CFT duality, these loops map to surfaces which are 'pseudo-holomorphic' with respect to a novel almost-complex structure defined on a suitable subspace of AdS5xS5. Of particular interest is the subclass of loops lying on a two-sphere in space-time whose expectation value is conjectured to be computed exactly in terms of the analogous observables in bosonic 2d Yang-Mills on S2. Several evidences for this conjecture, both on the gauge theory and on the string theory side will be discussed.

The hidden on-shell E(7(7)) symmetry of maximal supergravity is usually discussed in a truncation from D=11 to four dimensions. In my talk, I will reverse this logic and start from a theory with manifest off-shell E(7(7)) symmetry inspired by West's coset construction. I will start with a short motivation of the generalized coset dynamics by explaining the procedure of symmetry enhancement for the familiar example of general relativity. Maximal supergravity will then be related to an extension of this procedure, whose dynamics takes place in a 4+56 dimensional exceptional geometry, following de Wit and Nicolai. Requiring a bosonic symmetry enhancement will be shown to uniquely fix the couplings in the Lagrangian as well as potential supersymmetry variations for the 56 dimensional subsector. Truncating this theory to seven dimensions exactly coincides with the truncation of both the dynamics and the supersymmetry variations of D=11supergravity in a truncation to d=7 and in the restriction to the bosonic fields contained in the Cremmer-Julia coset E(7(7))/SU(8).

We present a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar N=4 SYM theory. It takes the form of a Y-system based on the integrability of the dual superstring sigma-model on the AdS5 x S5 background. This Y-system passes some very important tests: it reproduces the full asymptotic Bethe ansatz at large L, including the dressing factor, and it confirms all recently found wrapping corrections. We shall also describe the derivation of these equations in some detail.

The hierarchy problem can be represented as a tension between the need for a large cut-off scale suggested, for instance, by flavor physics and the need for a low cut-off scale suggested by naturalness in electroweak symmetry breaking. I will illustrate how this tension could be largely alleviated if the Standard Model flowed to an approximate CFT above the weak scale with a specific relation among the scaling dimensions of the Higgs sector fields. To investigate the viability of that scenario one is led to ask the following simple question: in an arbitrary CFT, given a scalar operator phi, and the operator S=phi phi defined as the lowest dimension scalar S which appears in the OPE phi phi, what is the bound (that is d(S) is smaller than f(d(phi))) on the scaling dimensions of the two operators? I will present a derivation of the bound based on general considerations of OPE, conformal block decomposition, and crossing symmetry. The function f(d(phi)) is computed numerically. When d(phi) goes to 1, one has f(d(phi))=2+O(sqrt(d(phi)-1)), which shows that the free theory limit is approached continuously. An analogous bound can be derived in 2D where some non-trivial consistency check can be made. I will discuss the relevance of the result for the hierarchy problem and illustrate the directions of future investigation.

Brane Tilings are known to describe the largest known class of SCFT's in 3+1 dimensions. There is a well established formalism to find AdS_5 x SE_5 duals to these SCFT's and to compare results on both sides. This talk extends this formalism to 2+1 dimensional SCFT's, living on the world volume of M2 branes, which are dual to AdS_4 x SE_7 backgrounds of M theory. The SCFT's are quiver gauge theories with 4 supercharges (N=2 in 2+1 dimensions) and Chern Simons (CS) couplings. They admit a moduli space of vacuum configurations which is a CY4 cone over SE_7. The talk will go over the formalism and look at several examples in detail. The computation of scaling dimensions will be mentioned and relations to regular toric Fano 3-folds if time permits.

This talk briefly explains why finding the vacuum solutions of gauged maximal supergravity models is a mathematically challenging problem, and which techniques exist that are powerful enough to actually solve it. As these techniques require joint effort between physicists and computer scientists, the problem is explained in a way that should be accessible to both groups. In models of extended supergravity with more than one gravitino, the symmetry group transforming the gravitini into one another can be promoted to a local symmetry. In order to maintain supersymmetry, such a deformation mandates the introduction of a potential for the scalar fields whose stationary points correspond to vacua with spontaneously broken symmetry. The most famous such model is the SO(8)-gauged N=8 supergravity in four dimensions by de Wit and Nicolai, which also can be obtained by dimensional reduction of M-theory on the 7-sphere. The mathematical problem in the determination of the vacua lies in the complexity of the potential, which is a function on a high-dimensional Riemannian symmetric space based on an E-series exceptional Lie group. While previous group theoretic arguments allowed a partial investigation of the problem only, there are powerful semi-numeric computational techniques that indeed seem to be strong enough to solve the problem in full. These methods are explained using as an example the most challenging supergravity potential, that of N=16 in D=3 with SO(8)xSO(8) gauge group, and some first data on new vacua of N=8 supergravity in D=4 are presented.