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Session 9
Tensor and Group Field Theories for Quantum Gravity
Chair:
Vincent Rivasseau (University Paris-Sud, France)
Titles and Abstracts
Joseph Ben Geloun (Perimeter Institute for Theoretical Physics, Canada)
Title: Asymptotic freedom of the renormalizable fourth rank tensor field theory
Abstract: The rank four renormalizable tensor field theory over U(1)^4 generating
simplicial pseudo-manifold in four 4d will be reviewed. Furthermore, the beta
functions for the different couplings and the asymptotic freedom of the model will be
discussed.
Razvan Gurau (Perimeter Institute for Theoretical Physics, Canada)
Title: Universality for random tensors
Abstract: In this talk I will explain why the Gaussian distribution for random tensors is
universal at large N, that is any uniformly bounded trace invariant tensor distribution
converges to a Gaussian.
Mikhail Katanaev (Steklov Mathematical Institute, Russia)
Title: Three dimensional gravity, dislocations, and the Riemann-Hilbert problem
Abstract: The expression for the free energy of arbitrary static distribution of wedge
dislocations is proposed. In the framework of geometric theory of defects, the free
energy is given by the Euclidean action for (1+2)-dimensional gravity interacting with
point particles. Relative movement of particles in gravity corresponds to bending of
dislocations. The equations of equilibrium are analyzed and reduced to the
Riemann-Hilbert problem. For two dislocations, the solution is found explicitly
through hypergeometric functions.
Thomas Krajewski (Centre de Physique Théorique, Marseille, France)
Title: Schwinger-Dyson equations in group field theory models of quantum gravity
Abstract: Building on earlier work of Gurau, we derive the general form of the
Schwinger-Dyson equations for the boundary states in group field theory. We further
discuss their mathematical structure as well as their physical implications.
Daniele Oriti (Albert Einstein Institute, Germany)
Title: The quantum geometry of group field theories
Abstract: We present recent results in group field theory models of quantum gravity in
3 and 4 dimensions, all having to do with the correct encoding of quantum (simplicial)
geometry. These include: the formulation of GFTs as non-commutative field theories
on Lie algebras; the relation between the star product used in such formulation and the
quantization of the phase space of the underlying simplicial structures; the construction
of 4d gravity models on this basis, and the properties of their amplitudes, both as
simplicial gravity path integrals and as spin foam models; the (quantum group)
symmetries of the same models and their relation to discrete diffeomorphisms.
James Ryan (Albert Einstein Institute, Germany)
Title: A glimpse at the future of tensor models
Abstract: In recent times, there has been an explosion of interest in tensor models and
their related field theories. Current research can be divided to a certain extent along two
lines. The first regards the development of a broad array of techniques to study generic
tensor theories, in particular, the adaptation of both matrix model and renormalization
group techniques. The second regards the utilization of these tensorial tools to study
dynamical systems, in particular, quantum gravity and matter systems of interest in
statistical mechanics. I shall present an overview of these research directions,
concentrating strongly on the developments we are likely to see in the coming years.
Naoki Sasakura (Kyoto University, Japan)
Title: Canonical tensor model with local time and its uniqueness
Abstract: A canonical formulation of the rank-three tensor model with a notion of
local time is proposed. The consistency of the local time is guaranteed by a first-class
constraint algebra. In a limit of localized configurations, the algebra formally
approaches the DeWitt algebra of the general relativity. The uniqueness of the model
can be shown on some physically reasonable assumptions. The quantization of the
model is straightforward, and some preliminary results on its dynamics for small N are
briefly reported.
Zhituo Wang (University of Paris-Sud, France)
Title: Construction of the two dimensional Grosse-Wulkenhaar model
Abstract: The 2-dimensional Grosse-Wulkenhaar model is a super-renormalizable
scalar field theory defined on the 2 dimensional noncommutative Moyal plane. I shall
prove the Borel summability of the perturbation series of the Schwinger’s function with
the method of loop vertex expansion, which could be also useful for the construction of
tensor models.