## Jan Ambjorn

### DT and CDT, theories of quantum geometry?

I discuss to what extent Dynamical Triangulations and Causal Dynamical Triangulations can be used to define a theory of quantum gravity, or more generally “theories of quantum geometries”. This covers new studies of 4d DT as well as RG flows in 4d CDT.

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**David Andriot**

### (Non)-geometry and non-geometric fluxes (slides)

I will start by reviewing the string theory notion of non-geometry, from various perspectives: in ten-dimensional standard supergravity, in doubled geometry, Double Field Theory and its exceptional generalizations, in Generalized Complex Geometry, and finally at the world-sheet level, where non-commutativity and non-associativity occur. I will then come back to the notion of four-dimensional non-geometric fluxes, and show how ten-dimensional beta-supergravity provides an uplift for them, while restoring a standard geometry from a non-geometry. Toroidal examples and NS-branes will illustrate the discussion.

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### Dario Benedetti

### One-loop renormalization in a toy model of Horava-Lifshitz gravity (slides)

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### Joseph Ben Geloun

### Tensor Models/Group Field Theories: An overview (slides)

From motivations to technical renormalization aspects, passing through some combinatorial problems emerging through their study, a progress report on tensorial models/group field theories for gravity will be given. Future investigations and challenges for this approach will be listed.

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### Freddy Cachazo

### Scattering Equations: From Riemann to Feynman (paper)

The scattering matrix of gravitons is well defined at least at tree level in any number of dimensions and it can be computed using Feynman diagrams. The S-matrix is a function in the space of Mandelstam variables with singularities determined by locality and unitarity. In this talk, we replace this space by the space of punctured Riemann spheres (PRS) and show how the two are connected by the “scattering equations”. Finally, a compact formula for the full tree-level S-matrix is given as an integral over the space of PRS localized to solutions to the scattering equations.

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### Francois David

### Discrete and continuum 2 dimensional quantum gravity (slides)

I present a new model of dynamical planar triangulations. It exemplifies the relations between conformal discrete geometries (circle patterns, conformal point processes), Kähler geometry and ideal tessellations in H3=AdS3, and 2D quantum gravity (non-critical strings, Liouville theory and topological 2D gravity).

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### Emilian Dudas

### Flavor models in supersymmetry (slides)

We review flavor constraints and models based on family symmetries addressing them in supersymmetric extensions of the Standard Model. We discuss explicitly the minimal supersymmetric extension of the Standard Model (MSSM) and also extensions where the fermionic superpartners of the gauge fields are of Dirac type.

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### Jurek Lewandowski

### Loop Quantum Gravity Coupled to a scalar field

Two canonical frameworks designed to couple LQG with scalar field will be discussed. In the first of them the scalar field is used for a deparametrization of the theory. In the consequence it disappears from the theory swallowed by the other degrees of freedom. In the second framework, the scalar field is explicitly present in the Hamiltonian of the system. New elements presented in this talk are a quantum scalar field energy operator and the quantum Ricci scalar operator. They were derived by the speaker together with Hanno Sahlmann, and, respectively, with Mehdi Assanioussi and Emanuele Alesci.

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### Jan Manschot

### Black hole bound states (slides)

I will discuss recent progress on the understanding of the quantum bound states of supersymmetric black holes. Two complementary descriptions exist: the Coulomb branch in terms of a solution space of bound states, and the Higgs branch in terms of the cohomology of quiver moduli spaces. I will explain how one can determine explicitly the number of quantum states (the BPS index) for arbitrary sets of constituents as function of the “single centered indices”. A single centered index enumerates the quantum states of a single constituent. I will furthermore describe a generalized mutation symmetry which relates bound states with different sets of constituents and single centered indices.

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### Marcos Marino

### Quantum Corrections in Supergravity and Exact Results in AdS/CFT

The AdS/CFT correspondence provides in principle a description of quantum gravity and M-theory on certain backgrounds, in terms of gauge theories in the 1/N expansion. Although this opens the possibility to study quantum aspects of gravity in terms of gauge theories, most of the work on the AdS/CFT correspondence has focused on the classical limit of the correspondence. Recently, a combination of localization and 1/N techniques has made it possible to calculate the full 1/N expansion of the Euclidean partition function for a class of gauge theories with supergravity duals. In this talk I present these exact results, I extract their implications and predictions for quantum corrections in supergravity, and I describe a successful one-loop test of these predictions. I also show that there is a very rich structure of non-perturbative corrections at large N in the gauge theory, which are due to extended objects in the M-theory dual.

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### Sameer Murthy

### Exact quantum entropy of black holes: a macroscopic view into quantum gravity (slides)

The pioneering work of Bekenstein and Hawking in the 70’s produced a universal area law for black hole entropy valid in the infinite size limit. Quantum corrections to the gravitational action induce finite size corrections to the black hole entropy. I shall report on progress in the computation of the \emph{exact} quantum entropy of supersymmetric black holes in supergravity, using localization techniques. In simple examples in string theory, one has a solvable dual microscopic description as an ensemble of microscopic excitations. I shall describe how the gravity functional integral leads to the microscopic \emph{integer} degeneracies of this black hole, and its associated number theoretic properties.

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### Renaud Parentani

**Statistical interpretation in Quantum Cosmology (slides)**

It is generally assumed that the Born statistical interpretation applies to quantum cosmology/gravity. Yet, a careful analysis of the solutions of the Wheeler-DeWitt equation shows that this cannot be the case. In fact, the WDW equation predicts that the statistical interpretation should be conceived as a emergent quantity, as that of the background metric.

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### Aldo Riello

### The melon graph in the EPRL-FK spinfoam model (slides)

The most relevant evidences in favour of the Lorentzian EPRL-FK spinfoam model come from its capibility of reproducing the expected semiclassical limit in the large spin regime. The main examples of this are the large spin limit of the vertex amplitude, later extended to arbitrary triangulations, and that of the spinfoam graviton propagator, which was calculated on the simplest possible two complex. The relevance of such promising results may be endangered by the effects associated to radiative corrections. During this presentation, I will focus on the role played by the simplest diverging graph, the so called ‘melon graph’, which is known to play a fundamental role in tensorial group field theories. In particular, I will discuss its most divergent part and its geometrical interpretation. I will finally comment on the result, with particular attention to its physical consequences, especially in relation with the semiclassical limit of the spinfoam graviton propagator.

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### Gilles Schaeffer

### Regular coloured graphs of positive degree

The colored tensor model is a tentative higher dimensional analog of the well known random matrix models: in particular it admits a 1/N-expansion in terms of regular colored graphs of increasing degree, similar to the 1/N-expansion of matrix models in terms of ribbon graphs of increasing genus. These regular coloured graphs are dual representations of pure colored D-dimensional complexes, and they can be classified with respect to an integer, their degree, much like ribbon graph are characterized by the genus of the underlying surface.

The dominant term in their 1/N-expansion is known to involve melonic graphs, and first sub-dominant term has been recently described. In this join work with Razvan Gurau, we describe the complete series of sub-dominant terms: We analyse the structure of regular colored graphs of fixed positive degree and perform their exact and asymptotic enumeration. In particular we show that the generating function of the family of graphs of fixed degree is an algebraic series with a positive radius of convergence, independant of the degree. We describe the singular behavior

of this series near its dominant singularity, and use the results to establish the double scaling limit of colored tensor models.

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### Adrian Tanasa

### Combinatorics of multi-orientable random tensor models (slides)

Multi-orientable tensor models are a quantum field theoretical generalization of the celebrated colored tensor models. In this talk I will introduce the multi-orientable models and then present the main results related to their recently-obtained large N asymptotic expansion (N being the size of the tensor): leading order, next-to-leading order and finally some considerations on the combinatorics of the general term of this expansion.

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### Raimar Wulkenhaar

### Exact solution of the quartic matrix model (slides)

We show that the quartic matrix model with partition function Z[E,J]=\int dM exp(trace(JM-EM^2-(\lambda/4)M^4) is exactly solvable in terms of the solution of a non-linear equation and the eigenvalues of the external matrix E. Because of its striking similarity to the Kontsevich model, this solution could be of interest for 2D quantum gravity. On the other hand, the \lambda\phi^4_4 model on Moyal space is of this type, and our solution leads to the construction of Schwinger functions on R^4 which satisfy growth, covariance and symmetry and, with numerical evidence for -0.39<\lambda<=0, reflection positivity of the 2-point function.