Renormalization Group Approaches to Quantum Gravity Conference - Apr. 22-25th
I present recent work on the double scaling limit of random tensor models through the analysis of their Schwinger-Dyson equations. This study exemplifies their potential for probing the continuum phase structure of these theories.
Quartic tensor models can be rewritten in terms of intermediate matrix fields. The corresponding expansion is not only simpler, it suggests also new bridges between matrices, strings and tensors.
I will start with a brief overview of tensorial group field theories with gauge invariant condition and their relation to spin foam models. The rest of the talk will be focused on the SU(2) theory in dimension 3, which is related to Euclidean 3d quantum gravity and has been proven renormalizable up to order 6 interactions. General renormalization group flow equations will be introduced, allowing in particular to understand the behavior of the relevant couplings in the neighborhood of the Gaussian fixed point.
The entanglement entropy associated with a spatial boundary in quantum field theory is ultraviolet divergent, its leading term being proportional to the area of the boundary. Callan and Wilczek proposed a geometrical prescription for computing this entanglement entropy as the response of the gravitational effective action to a conically singular metric perturbation. I argue that the Callan-Wilczek prescription is rigorously justified at least for a particular class of quantum states each expressible as a Euclidean path integral.
I will argue that a fundamental theory of quantum gravity that is applicable to our universe must include matter degrees of freedom. In my talk I will focus on the option that these are fundamental, in contrast to low-energy effective, degrees of freedom, and must thus be included in the microscopic dynamics of spacetime.
We briefly review the various components and their conceptual status of the full Asymptotic Safety Program which aims at finding a nonperturbative infinite-cutoff limit of a regularized functional integral for a quantum field theory of gravity. It is explained why in the continuum formulation based on the Effective Average Action the key requirement of background independence unavoidably results in a "bi-metric" framework, and recent results on truncated RG flows of bi-metric actions are presented.
The role of time and a possible foliation structure of spacetime are longstanding questions which lately received a lot of renewed 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, I will discuss first results concerning the RG flow of
Horava-Lifshitz gravity, highlighting a possible mechanism for a dynamical Lorentz-symmetry restoration at low energies.
I will present some recent results on the UV properties of a toy model of Horava-Lifshitz gravity in 2+1 dimensions. In particular, I will illustrate some details of a one-loopcalculation, leading to beta functions for the running couplings. The renormalization group flow obtained in such way shows that Newton's constant is asymptotically free. However, the DeWitt
Quantum gravity with anisotropic scaling exhibits a rich structure of phases and phase transitions, dominated by multicritical behavior dependent on the spacetime dimension and the dynamical critical exponent. I will discuss some features of this phase structure, as well as its similarities and differences in comparison to the CDT approach to quantum gravity.
In this talk we discuss some notion of coarse graining in state-sums, most notably a class of spin foam models in their holonomy representations. We discuss the notion of scale in this context, and how diffeomorphism-invariance ties into the existence of a continuum limit. We close with an example and muse about the interplay between diffeomorphism-invariance and non-renormalizability.
©2012 Institut Périmètre de Physique Théorique