I will explain a gradient formula for beta functions of two-dimensional quantum field theories. The gradient formula has the form derivative c = - (gij+Delta gij+bij) bj where bj are the beta functions, c and gij are the Zamolodchikov c-function and metric, bij is an antisymmetric tensor introduced by H. Osborn and Delta gij is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to non-linear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.

Freed-Witten anomaly is a global ambiguity of the string path integral measure in the presence of D-branes. It turns out it uniquely determines, by imposing its cancellation, the topological type of both the A and the B fields when restricted to the brane, as it naturally involves the interplay between open and closed string degrees of freedom. After introducing the suitable mathematical framework provided by the theory of gerbes with connections, I will try to characterize the nature of the gauge bundle on a brane in the most general closed string background. Furthermore, I will go over a case by case analysis, focusing on how it can account for fractional RR and Page charges and showing the physical relevance of the resulting K-theoretical improvement for classifying D-brane charges. Reference: L. Bonora, F. Ferrari Ruffino, R. S., arXiv: 0810.4291

The mini-superspace quantization of D=11 Supergravity is equivalent to the quantization of a E10-K(E10) coset space sigma model when the latter is restricted to the E10 Cartan subalgebra. As a consequence, the wavefunctions solving the relevant mini-superspace Wheeler-DeWitt equation involve automorphic (Maass wave) forms under the modular group W+(E10) cong PSL2(O). Using Dirichlet boundary conditions on the billiard domain a general inequality for the Laplace eigenvalues of these automorphic forms can be derived, which implies that the wave function of the universe is generically complex and always tends to zero when approaching the initial singularity. The potential significance of these properties for the question of singularity resolution in quantum cosmology is discussed, also in comparison with other approaches. The present approach offers interesting new perspectives on some long-standing issues in canonical quantum gravity.

The Romans mass is a discrete parameter in type IIA string theory. It is perhaps the most mysterious piece of the theory: for example, its non-perturbative, M-theoretic interpretation is still not known. In this talk, we will review recent efforts to understand it through another non-perturbative tool: holography. We will see how this parameter modifies the recent holographic interpretation of certain string vacua via Chern-Simons theories. This leads to certain field theory results that, in turn, help find new families of supersymmetric vacua of string theory with negative cosmological constant.

I will review the construction of BPS and non-BPS multicenter black hole solutions, and describe a class of smooth solutions that have the same charges and asymptotics as black holes, but do not have a horizon. I will then discuss some of the properties of these solutions and argue that they should correspond to typical microstates of extremal black holes. If so, string theory would imply that a classical extremal black hole solution is a thermodynamic approximation of an ensemble of horizonless configurations, and that this solution stops giving a valid description of the physics at the scale of the horizon. I will finish by discussing the extension of this to non-extremal black holes and its implications for the information paradox.

We give a method of deriving the field-strengths of all massless and massive, i.e. gauged, maximal supergravity theories in any dimension starting from the Kac-Moody algebra E11. Considering the subalgebra of E11 that acts on the fields in the non-linear realisation as a global symmetry, we show how this is promoted to a gauge symmetry enlarging the algebra by the inclusion of additional generators. Given the enlarged algebra corresponding to the massless theory, we show that this can be deformed to obtain the algebra corresponding to the gauged theory. We show how this works in detail for the case of Scherk-Schwarz reduction of IIB to nine dimensions. We then classify all the possible deformations in any dimensions and show that these are in one to one correspondence with all the possible gauged supergravities. This provides a very efficient, simple and unified derivation of the field strengths and gauge transformations of all the bosonic fields of any maximal supergravity theory.

I will discuss recent progress in understanding non-geometric string backgrounds. These are inherently stringy constructions that are globally well- defined only up to T-dualities. One approach in analyzing such backgrounds is through the corresponding effective gauged supergravities. The classification of the latter in terms of embedding tensors provides us with a picture of the landscape of such backgrounds, realized in terms of non-geometric fluxes. Also, it is by now evident that a doubling of the coordinates of the underlying geometry is necessary for describing these backgrounds, since their stringy nature implies that winding modes should be treated on equal footing with the momentum modes. This leads us to doubled geometries and in particular twisted doubled tori, that are expected to underlie general supergravity gaugings. Of particular interest is the worldsheet description of such doubled geometries which involves chiral boson models. Although these models are not Lorentz invariant in general, for the twisted doubled tori Lorentz invariance is restored. Furthermore, the conditions for conformal invariance of those models agree with the conditions from minimizing the corresponding supergravity potential. This result firmly establishes that chiral boson models with twisted doubled tori target spaces are the worldsheet theories underlying a very broad class of supergravity gaugings.

We study various matrix models as toy models of the gauge dual of the AdS spacetime and black hole. I will summarize what these matrix models teach us about the information paradox and emergence of the light speed limit.

I will present a phenomenological model of the quark-gluon plasma that stem from 5 dimensional holography. The model is superior to the previous 5D models as it incorporates the running of the gauge coupling. It is constructed by requirements from QCD and a few lattice data. I will describe the transport properties of the quark-gluon plasma such as the bulk viscosity, energy loss of heavy quarks etc and their effects on the observables.

We will discuss a direct prescription for computing the mixing among gauge invariant operators in N=4 SYM. This approach is based on the action of the superalgebra on the states of the theory and circumvents the problem of diagonalising the dilatation matrix. As an example, we will derive the leading and subleading planar quantum corrections to the BMN-like operators belonging to the supermultiplet with 2 impurities. Furthermore, we will discuss the relation to Beisert's SU(2,2) dynamic S-matrix approach. The same method can be applied in the BMN limit of the dual string description. The string theory expressions for the states match nicely the field theory ones up to order lambda'. We will also focus on the implications of the mixing terms for 3-point functions of 2 BPS and one non-BPS operator. Namely, should the mixing terms were not there, constraints following from the superconformal and the bonus U(1)Y symmetries would be violated. Subsequently, we will utilise the BMN limit of the AdS5xS5 string theory to analyse the string amplitudes corresponding to the 3-point functions studied above. The mixing is again crucial to ensure the cancellation of various amplitudes that would otherwise violate symmetry constaints. However,on the string side, we find examples of interactions which violate expectations coming from superconformal Ward identities and the U(1)Y symmetry. Finally, we will comment on the possible resolution of this mismatch.

We review some results concerning integrable systems on the moduli spaces of holomorphic bundles. The interrelations between bundles of different topological types are given by modifications (singular gauge transformations). The modification provides canonical maps between corresponding integrable systems. It also allows to describe the Backlund transformations. We apply the general scheme to the elliptic Calogero-Moser model and construct a map to an integrable Euler-Arnold top (the elliptic SL(N)-rotator). The models correspond to the bundles of degree zero and one. Explicit formulae represent a bosonization of the coadjoint orbit. The later describes the phase space of the rotator while the Poisson structure of the Calogero model is canonical. The construction can be generalized to more complicated models. For example, field generalization (loop group or 1+1 theories) leads to relation between the field Calogero model and the Landau-Lifshitz equation for XYZ model while the generalization to the isomonodromic deformations leads to relation between Painleve VI equation and Zhukovsky-Volterra gyrostat. In the end we note that the classification of models is described by the center of the structure group which are shown to be characteristic classes of the bundles. This remark allows to generalize the construction to the case of an arbitrary simple Lie group. Three-dimensional generalization of the construction naturally leads to the Bogomolny equations. The modification in this case provides non-trivial charge of the monopole solution. We find the Dirac monopole solution in the case (R)x(Elliptic curve). This solution is a three-dimensional generalization of the Kronecker series. We give two representations for this solution and derive a functional equation for it.

We review some results concerning integrable systems on the moduli spaces of holomorphic bundles. The interrelations between bundles of different topological types are given by modifications (singular gauge transformations). The modification provides canonical maps between corresponding integrable systems. It also allows to describe the Backlund transformations. We apply the general scheme to the elliptic Calogero-Moser model and construct a map to an integrable Euler-Arnold top (the elliptic SL(N)-rotator). The models correspond to the bundles of degree zero and one. Explicit formulae represent a bosonization of the coadjoint orbit. The later describes the phase space of the rotator while the Poisson structure of the Calogero model is canonical. The construction can be generalized to more complicated models. For example, field generalization (loop group or 1+1 theories) leads to relation between the field Calogero model and the Landau-Lifshitz equation for XYZ model while the generalization to the isomonodromic deformations leads to relation between Painleve VI equation and Zhukovsky-Volterra gyrostat. In the end we note that the classification of models is described by the center of the structure group which are shown to be characteristic classes of the bundles. This remark allows to generalize the construction to the case of an arbitrary simple Lie group. Three-dimensional generalization of the construction naturally leads to the Bogomolny equations. The modification in this case provides non-trivial charge of the monopole solution. We find the Dirac monopole solution in the case (R)x(Elliptic curve). This solution is a three-dimensional generalization of the Kronecker series. We give two representations for this solution and derive a functional equation for it.

There is good evidence that a class of conformal gauge theories at strong gauge coupling and for large rank of the gauge group can be described by classical gravity in five dimensions. In this gauge/gravity duality, the theory of classical gravity always admits a consistent truncation to pure gravity so that there is a sector in the dual gauge theories where the dynamics is universal. This universal sector constitutes phenomena like hydrodynamics, but also other phenomena far away from equilibrium such as decoherence and relaxation. We will use field theoretic tools to understand how the time evolution of all states and the expectation values of all observables in the universal sector get determined by the energy-momentum tensor alone. We will find a way to extrapolate our field-theoretic results to strong coupling to propose a condition on the energy-momentum tensor such that the dual solution in gravity has a smooth future horizon, as a test of our approach. We will also do a first study of how irreversibility emerges at long time scales of observation through gravity.

AdS2-CFT1 correspondence leads to a prescription for computing the degeneracy of a single centered extremal black hole in terms of path integral over string fields living on the near horizon geometry of the extremal black hole. This prescription is called quantum entropy function. In four dimension the near horizon isometry group SL(2,R) x SU(2) for BPS black hole gets enhanced to full SU(1,1,2). Using these enhanced supersymmetries and localization techniques, we will argue that the path integral receives contribution only from special class of field configurations which are invariant under a particular subgroup of SU(1,1,2). We will identify saddle points which are invariant under this subgroup.

Over the last years, gauge/string duality has been extended to include gauge theories with an arbitrary number of flavors. We study the flavoring procedure in the light of calibrated geometry and discuss the special case of a type IIA dual of N=1 super Yang-Mills with flavors. Relating our results to the standard type IIA/M-theory duality, we find that the usual oxidation formulas cannot accommodate for the additional flavor branes. We address and solve this issue by considering M-theory with torsion, which allows us to construct source-modified equations of motion for eleven-dimensional supergravity.

Solvmanifolds, in particular nilmanifolds, commonly known as twisted tori, provide several examples of internal manifolds in flux compactifications towards de Sitter, Minkowski or Anti de Sitter. The relation between these manifolds and the six-dimensional torus, and the string vacua obtained on them, are the main interests of this talk. We will first present some properties of these manifolds. We will give a generic construction of their Maurer-Cartan forms out of the six-dimensional torus, via a transformation called the twist. We will then describe several Minkowski flux backgrounds of type II supergravity obtained on these manifolds. Thanks to the generalized complex geometry approach, we will show that one can obtain those solutions from solutions on the torus, via the twist transformation. The latter then acts as a solution generating technique, being able to relate backgrounds which are not T-duals. Finally, we will apply this twist transformation technique to relate Kahler/non-Kahler solutions of the heterotic string. This talk is based on a work with Enrico Goi, Ruben Minasian and Michela Petrini.

I talk about finite corrections to the large spin asymptotics of N=4 SYM twist operators. These corrections are an all-loop result, not affected by wrapping effects, and agree, after determining the strong coupling expansion, with string theory predictions. The finite order corrections enter the sub-leading poles of the logarithm of multi loop gluon scattering amplitudes and describes the difference between the former and the expectation value of certain Wilson lines. For the complete sub-leading pole structure however a second function is needed. A few comments on the quest for a search of a possible description of the latter in terms of local operators will be given.

We review the derivation of a 6d gauge theory related to the M5 brane from the Bagger-Lambert-Gustavsson (BLG) model with the volume preserving diffeomorphisms gauge group. In particular, the Lagrangian for the 6d self-dual antisymmetric tensor field appears upon converting three of eight scalars in the BLG theory into the components of antisymmetric tensor field in D=6. We develop also a Lorentz-covariant Lagrangian formulation for such an antisymmetric tensor field in the free case. This formulation admits a natural supersymmetrization as well as coupling to 6d gravity.