Quantum Gravity

I will review recent work on tensorial group field theories (TGFTs). The renormalization methods being developed in this context provide more and more control over their field-theoretic structures, and for models which increasingly resemble loop quantum gravity. Perhaps surprisingly, some of these models are asymptotically free and can therefore be made sense of at arbitrary values of the (abstract) scale with respect to which they are organized. They define in this sense UV complete quantum field theories. I will focus on TGFTs with gauge invariance condition, which allow for such a behavior but also for more complicated scenarii involving non-trivial fixed points of the renormalization group flow. I will finally comment on the physical relevance of this notion of UV completion.

It is by now well established that black holes emit a thermal radiation and undergo an evaporation process. The original Hawking evaporation scenario, based on quantum fields on a classical background geometry, has been vastly extended and improved, in order to take into account in particular the backreaction of the radiation on the geometry. This can be done for example in a semiclassical setup, where the Einstein equations are sourced by an effective stress energy tensor. In two-dimensional models, this is a powerful method since the conformal anomaly enables one to reconstruct unambiguously the full effective stress energy tensor, or the corresponding effective matter action. However, attempts to generalize this method in four dimensions have been so far partly unsuccessful. In this talk we will review the difficulties that arise in attempts to constructing the effective action for matter fields coupled to a dilaton, and focus on a potential way out of the problem. This could lead to a new expression for the effective stress energy tensor on a black hole geometry, and to progress in the the study of backreaction in four-dimensional spherically symmetric models.

I present a proposal for a worldline action for discretized gravity with the same field content as loop quantum gravity. The proposal is defined through its action, which is a one-dimensional integral over the edges of the discretization. Every edge carries a finite-dimensional phase space, and the evolution equations are generated by a Hamiltonian, which is a sum over the constraints of the theory. I will explain the relevance of the model, and close with possible relations to other approaches of quantum gravity, including: relative locality, causal sets and twistor theory.