Approaches to Quantum Gravity, Clermont-Ferrand, Jan. 6-10th 2014


Monday, Jan. 6th

Tuesday, Jan. 7th

Wednesday, Jan. 8th

Thursday, Jan. 9th

Friday, Jan. 10th

9h00 Coffee

10h00 K. Noui I

10h00 V. Rivasseau II

10h00 G. Catren

10h00 K. Rejzner

10h00 M. Sakellariadou

11h30 V. Rivasseau I

11h30 J. Henson II

11h30 F. Saueressig

11h30 V. Bonzom

11h30 J. Henson III

12h45 Lunch

12h45 Lunch

12h45 Lunch

12h45 Lunch

12h45 Lunch

14h15 J. Henson I

14h15 D. Benedetti II

14h15 D. Litim

14h15 G. Bossard

14h15 V. Rivasseau III

15h30 D. Benedetti I

15h30 K. Noui II

15h45 K. Noui III

15h45 D. Benedetti III

17h00 T. Budd

17h00 R. Gurau

Wednesday 8th, 20h00 : conference dinner.

Titles and abstracts

Dario Benedetti (A. Einstein Institute, Golm)

Causal dynamical triangulations and their interpretation in the continuum.

Causal dynamical triangulations are a statistical model of fluctuating discrete geometries, and an important candidate for a nonperturbative quantum theory of gravity. In these lectures I will begin by reviewing the motivations and general ideas behind such models, in particular conceptually placing them within the asymptotic safety scenario. I will then proceed by illustrating the explicit construction of the models, starting from the non-causal ones, presenting a selection of analytical results in some detail, and briefly reviewing some numerical results. Finally I will try to make contact with other approaches that work directly in the continuum in a more familiar quantum field theory language, thus discussing the relation to the functional RG formulation of asymptotic safety and to Horava-Lifshitz gravity.

Joseph Henson (Imperial College, London)

An invitation to Causal Sets

Most quantum gravity researchers endorse the general idea that the properties of classical spacetime will become "fuzzy" or disintegrate entirely at or near the Planck scale, and many believe that classical spacetime itself only emerges as an approximation to a discrete underlying structure. But there are great difficulties in modelling such fuzziness without breaking or deforming local Lorentz Invariance. The causal set idea provides a way to do just that, giving us one clear way to model an emergent spacetime in keeping with the symmetries of GR, and perhaps a foundation of which to build a theory of quantum gravity. Theses lecture will explain how spacetime could be an approximation to a causal set, give some details on how to recover manifold concepts from the discrete structure, and explain some of the uses this concept has been put to in developing phenomenological models.

Lecture 1 : The causal set idea. How to recover the manifold from causal structure.

Lecture 2 : Some phenomenological arguments. How the cosmological constant was predicted. Modelling the effects of Planck-scale fuzziness on light and matter propagation.

Lecture 3 : More of fields on causal sets. Dynamics of causal sets. Outlook.

Karim Noui (Université de Tours)

Loop Quantum Gravity : Foundations and Applications.

Vincent Rivasseau (Université Paris Sud)

Random Tensors, Renormalization and Quantum Gravity.

Random tensors of higher rank generalize random matrices. Their associated tensorial field theories generalize non-commutative field theories. We discuss these models, their relevance to quantum gravity and their renormalization.

Valentin Bonzom (Perimeter Institute)

Quantizing Euclidean geometry via loop quantum gravity techniques: relationships to the Reidemeister torsion and to the pentagon identity of SU(2).

It has been a long standing conjecture that loop quantum gravity enables to solve some topological quantum field theories which are based on the properties of the moduli space of flat connections over manifolds of arbitrary dimension. In this talk I will explain the key steps which lead to that result, focusing on the interplay between physics and mathematics. I will present a very simple model which aims at quantizing flat spacetime, but which turns out to feature several interesting mathematical aspects. It is defined through an integral on the set of discrete SU(2) connections over a cellular complex, which can be related to the Reidemeister torsion, a classical invariant. From the Hamiltonian view point, that model really quantizes the standard trigonometric relations of Euclidean geometry (like the relations between the dihedral angles in a tetrahedron and the angles of its triangles) in the form of well-known equations from the representation theory of SU(2) like the pentagon (or Biedenharn-Elliott) identity.

Guillaume Bossard (CPHT, Ecole Polytechnique)

Amplitudes in string theory and supergravity.

I shall explain the construction of amplitudes in string theory and in supergravity. Although supergravity theories are not renormalisable by power counting, string theory provides an ultra-violet completion that determines the ambiguities associated to the infinitely many higher derivative counter-terms. I will review the present knowledge on these amplitudes and how supersymmetry and duality Ward identities permit to make sense of the quantum field perturbative series to some extend. I shall also mention the conceptual obstacles that have to be circumvented in string theory and in quantum field theory, respectively.

Timothy Budd (Niels Bohr Institute, Copenhagen)

Fractal dimensions of 2d quantum gravity.

After introducing 2d quantum gravity, both in its discretized form interms of random triangulations and its continuum description as Quantum Liouville theory, I will give a (non-exhaustive) review of the current understanding of its fractal dimensions. In particular, I will discuss recent analytic and numerical results relating to the Hausdorff dimension and spectral dimension of 2d gravity coupled to conformal matter fields.

Gabriel Catren (Université Paris 7 Denis Diderot)

On Cartan Connections and the Geometric Structure of Space-Time

We shall present the conception about the geometric structure ofspace-time that results from the theory of Cartan connections. Many fundamental ideas concerning our comprehension of the notion of space converge in the theory of Cartan connections, notably Klein’s Erlangen program, Weyl's program of a “purely infinitesimal geometry”, and the “equivalence principle” of local flatness in Riemannian geometry. With respect to their importance in gravitational physics, whereas Ehresmann connections are the geometric counterpart of the gauge fields of Yang-Mills theory, Cartan connections allow us to describe the geometry of space-time in such a way that the fundamental variable is not a metric but rather a connection. This reformulation opens the possibility of revisiting the project of understanding the gravitation interaction in terms of a gauge theory, that is as a theory that describes a dynamical connection on a fiber bundle over space-time.

Razvan Gurau (CPHT, Ecole Polytechnique)

Tensor models beyond the 1/N expansion

In this talk I will present two results concerning tensor models. I will first discuss how the 1/N expansion of tensor models can obtained in full mathematical rigour (without using the perturbative expansion). I will then present a second result, the recently obtained doubles scaling limit of tensor models.

Daniel Litim (Sussex University)


Katarzyna Rejzner (York University)

Background independence of quantum gravity in the framework of general local covariance

The framework of locally covariant quantum (and classical) field theory, proposed by R. Brunetti, K. Fredenhagen and R. Verch proved to be very successful in describing QFT on curved spacetimes. Moreover, using relative Cauchy evolution, one can incorporate into this formalism the notion of background independence of classical and quantum gravity. In this talk I will report on recent developments in investigating this problem. I will also show how gravity can be quantized as an effective theory in the locally covariant framework.

Mairi Sakellariadou (King's College, London)

Physics of the Spectral Action.

The unification of the four fundamental forces remains one of the most important issues in theoretical particle physics. In this talk, I will first give a short introduction to noncommutative spectral geometry, a bottom-up approach that unifies the (successful) Standard Model of high energy physics with Einstein's General theory of Relativity. The model is build upon almost-commutative spaces and I will discuss the physical implications of the choice of such manifolds. I will show that even though the unification has been obtained only at the classical level, the doubling of the algebra may incorporate the seeds of quantisation. I will then briefly review the particle physics phenomenology and highlight open issues and current proposals. In the last part of my talk, I will explore consequences of the gravitational-Higgs part of the spectral action formulated within such almost-commutative manifolds. In particular, I will study modifications of the Friedmann equation, propagation of gravitational waves and the onset of inflation. I will show how current measurements (Gravity Probe B and pulsars) can constrain free parameters of the model. I will then discuss the onset of inflation in the absence of an inflaton (scalar) field, through R^2 terms in the action. I will conclude with a short discussion on open questions.

Frank Saueressig (Univ. of Nijmegen)

Asymptotic safety - Relating the Functional Renormalization group and Causal Dynamical Triangulations

The role of time and the possibility of spacetime carrying a foliation structure are longstanding questions which lately received a lot ofrenewed attention from the quantum gravity community. In this talk, I will review recent progress in formulating a Wetterich-type functional renormalization group equation on foliated spacetimes and outline its potential applications. In particular, we will discuss first results concerning the RG flow of anisotropic gravity models and novel perspectives for recovering the phase-diagram obtained from Monte-Carlo Simulations of the gravitational partition sum based on the functional renormalization group.