The Bekenstein-Hawking formula for the entropy of a black hole suggests that entropy in strong gravity situations should be proportional to bounding area rather than enclosed volume. But we argue that the S and T dualities of string theory suggest an entropy formula that is extensive in the volume, with the area formula appearing as a special case. In particular we find a set of states in string theory that violate the covariant entropy bound, which seeks to extend the area entropy formula to situations like the early Universe.

By studying the cosmological dynamics of the moduli and axion fields we develop a set of "generic predictions" of solutions to string/M theory which have low energy supersymmetry breaking and grand unification. The nature of dark matter plays an important role in much of the discussion.

It is commonly believed that for a quantum field theory to be fundamental, its high-energy behaviour must be governed by an ultraviolet (UV) fixed point. A very satisfying example is given by asymptotic freedom of QCD where the UV fixed point is non-interacting. In this talk, I discuss the existence of interacting UV fixed points in various quantum field theories, in particular in four dimensions, both with and without gravity. Implications for particle physics are also evaluated.

We study the form factor of a generic gauge-invariant local composite operator in N=4 SYM theory. At tree-level and for a minimal number of external fields, the form factor exactly realises the spin-chain picture of N=4 SYM theory in the language of scattering amplitudes. Via generalised unitarity, we obtain the cut-constructible part of the one-loop correction to the minimal form factor of a generic operator. Its UV divergence yields the complete one-loop dilatation operator of the theory. We also compute the complete two-loop correction to the two-point form factor of the Konishi operator via unitarity and obtain the two-loop Konishi anomalous dimensions from it. For the Konishi operator as well as other non-protected operators, important subtleties arise which require an extension of the method of unitarity. Moreover, since the inclusion of non-protected operators into the action renders it formally non-supersymmetric, the form factors of these operators share many features with quantities in QCD, such as the occurrence of rational terms. The talk is based on the recent works 1410.6309 and 1410.8485.

In many instances of holographic correspondences between a d dimensional boundary theory and a d+1 dimensional bulk, a simple argument in the boundary theory implies that there must exist a direct relation between the on-shell Euclidean gravitational bulk action and the on-shell Euclidean action of a (d-1)-brane probing the bulk geometry. This relation is crucial for the consistency of holography but puzzling from the bulk perspective. We provide a full bulk derivation in the case of pure gravity. A central role is played by a non-trivial isoperimetric inequality that must be satisfied in a large class of Poincaré-Einstein spaces. Remarkably, this inequality follows from a theorem by John Lee.

Within the context of the duality between higher spin gravitational theories and a semi- classical limit of WN minimal models, we consider 2D CFTs with W1 symmetry at nite temperature, deformed by the presence of a chemical potential for the spin{three current. As a perturbative expansion in the chemical potential, we compute the Renyi and entanglement entropies for a single interval. The leading correction is universal and matches the holographic result, based on Wilson line functionals, obtained from the higher spin gravitational dual.

In this series of 4-5 2-hour lectures, I'll describe some of the powerful exact results that one can achieve in supersymmetric theories. The topics will be as follows: Lecture 1: Non-Renormalization Theorems Lecture 2: Classical and Quantum Moduli Spaces Lecture 3: Superconformal Field Theories and Seiberg Duality Lecture 4: Central Charges, a-maximization, and the a-theorem Lecture 5 (if it happens): Brane Tilings and Dimers

In recent years, due to the method of supersymmetric localization, many exact results have been achieved in the study of supersymmetric gauge theories on compact spaces of various dimension and topology, leading to the discovery of surpraising structures. An important example is provided by the correspondence introduced by Alday, Gaiotto and Tachikawa, relating the partition functions of a large class of supersymmetric gauge theories on S4 and S2 to correlators in Liouville CFT. In this talk, I will explain how this picture can be lifted to higher dimensional gauge theories via the correspondence of partition functions on S5, S4xS1, S3 and S2xS1 to correlators in theories whose underlying symmetry is given by a quantum deformation of the Virasoro algebra. In particular, I will discuss how 3-point functions can be derived by the bootstrap approach and used to define this novel class of q-deformed CFTs. I will also discuss some aspects related to integrable structures in these models, such as reflection coefficients, as well as possible generalisation.

In this series of 4-5 2-hour lectures, I'll describe some of the powerful exact results that one can achieve in supersymmetric theories. The topics will be as follows: Lecture 1: Non-Renormalization Theorems Lecture 2: Classical and Quantum Moduli Spaces Lecture 3: Superconformal Field Theories and Seiberg Duality Lecture 4: Central Charges, a-maximization, and the a-theorem Lecture 5 (if it happens): Brane Tilings and Dimers

In recent years there is a growing interest in unconventional string backgrounds with non-geometric fluxes. The latter often appear after repeated T-dualities on known backgrounds. However, a very interesting question regards whether these fluxes can coexist in generalized geometries without a geometric dual. In this talk we address this question and we show that in principle there exist such geometries where all types of fluxes coexist. Our strategy consists in using generalized geometry and in particular Dirac structures, which are subbundles of the generalized tangent bundle where the Courant bracket is associative and field strengths transform tensorially. We study the mathematical description of fluxes on Dirac structures and then combine the latter into Courant algebroids that describe multi-flux geometries. Furthermore we discuss the sources of non-geometric fluxes, which are heavy extended objects known as exotic branes. These branes exhibit a wide range of world volume dimensions, tension scalings and monodromy properties, and we argue that they couple to certain mixed symmetry tensors, which are exotic magnetic duals of the supergravity background fields.

Taking inspiration from lattice QCD data, we argue that a finite non-perturbative mass contribution for quarks is generated as another consequence of the dynamical phenomenon of spontaneous chiral symmetry breaking, which is in turn triggered by the explicitly breaking of chiral symmetry induced by the critical Wilson term in the action. In pure lattice QCD this mass term cannot be separated from the unavoidably associated linearly divergent contribution. However, if QCD is enlarged to a theory where also a scalar field is present, coupled to a doublet of SU(2) fermions via a Yukawa and a Wilson-like term, then in the phase where the scalar field takes a non-vanishing expectation value, a dynamically generated and "naturally" light fermion mass (numerically unrelated to the expectation value of the scalar field) is conjectured to emerge at a critical value of the Yukawa coupling where the symmetry of the model is maximally enhanced. Masses dynamically generated in this way display a natural hierarchy according to which the stronger is the strongest of the interactions the fermion is subjected to the larger is its mass.

In this series of 4-5 2-hour lectures, I'll describe some of the powerful exact results that one can achieve in supersymmetric theories. The topics will be as follows: Lecture 1: Non-Renormalization Theorems Lecture 2: Classical and Quantum Moduli Spaces Lecture 3: Superconformal Field Theories and Seiberg Duality Lecture 4: Central Charges, a-maximization, and the a-theorem Lecture 5 (if it happens): Brane Tilings and Dimers

In this series of 4 or 5 2-hour lectures, I'll describe some of the powerful exact results that one can achieve in supersymmetric theories. The topics will be as follows: Lecture 1: Non-Renormalization Theorems Lecture 2: Classical and Quantum Moduli Spaces Lecture 3: Superconformal Field Theories and Seiberg Duality Lecture 4: Central Charges, a-maximization, and the a-theorem Lecture 5 (if it happens): Brane Tilings and Dimers

We consider two classes of minimally supersymmetric STU-models in four dimensions motivated by their (conjectured) origin, respectively, from reductions of massive type IIA string theory on SU(3)-structure manifolds and M-theory on G2-structure. In both cases, we identify the geometric origin of the moduli ?fields and derive the dictionary between metric fluxes and torsion classes. The matching between the expression of the Ricci scalar and the metric flux-induced scalar potential works in any point of moduli space and regardless of whether or not Jacobi constraints have been imposed on the metric flux components. Finally, we provide the ten- or eleven-dimensional uplift of the aforementioned supergravity models by showing the equivalence between higher-dimensional and four-dimensional equations of motion.

The idea of writing supergravity as a double copy of super Yang-Mills theories has proved a fruitful one, most notably in the context of scattering amplitudes. I will explore this idea of "squaring" at a fundamental level to explain how the symmetries of the former(both local and global) can be written as a double copy of the latter. I will show how the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry are obtained from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincare. We give a gravity-gauge dictionary by convoluting fields and parameters. At the global level, I will explain how the coset groups of supergravity can be derived from the global R-symmetries of the SYM multiplets, via the 4 division algebras:reals, complexes, quaternions and octonions. Finally I will explore some intriguing possible applications of our dictonary.

A review will be provided on the renormalization program for the so-called Tensor Models for Quantum Gravity. These are non local field theories extending both the matrix models, a successful framework in statistical mechanics applied to 2D physics, and the Grosse-Wulkenhaar model in the matrix basis arising in Noncommuting Neometry. We will emphasize the Multi-scale renormalization but also report recent results on the Functional Renormalization Group Approach for these class of models.

I will present this very recently proposed geometric object, conjectured to give the N=4 SYM scattering amplitudes at all orders , and illustrate the techniques used to fully explore its structure. In so doing I will give firm nontrivial evidence to the amplituhedron conjecture.

It is well-known that infrared singularities arise in scattering amplitudes due to the emission of soft (low energy) gluons and / or gravitons. These are important for collider predictions, but also give us all-order insights into perturbation theory. This talk will review a number of recent developments in this area, such as: the structure of IR singularities in multiparton scattering amplitudes; the relationship between Yang-Mills theory and gravity in the soft limit; the classification of amplitudes beyond the soft approximation.