Quantum Gravity

Gravity possesses hidden symmetries that emerge upon dimensional reduction. One of the first examples being the Elhers SL(2,R) group revealed when reducing four-dimensional Einstein gravity to three-dimensions. However useful such symmetries are, especially to design solution generating techniques, they act in a highly non-local way on the gravitational data. On the other hand it is known that the solution space of asymptotically Flat spacetimes can be expressed covariantly in terms of an infinite number of tensors defined on the null conformal boundary. Therefore it is expected that hidden symmetries will act on the boundary data. In this talk, focusing on the simpler case of Petrov algebraically special spacetimes, I want to show that at the level of the boundary, the action becomes local, therefore much simpler, and makes explicit gravitational electric/magnetic dualities.

I plan to review several ways of testing if the gravitational field has quantum aspects in the low energy regime.  I explain why the hybrid (half quantum/half classical) models are inadequate and how they could be ruled out. Furthermore, I maintain that there is no prima facie reason to expect problems when quantizing gravity in the linear regime; I summarise the main perceived difficulties only to dismiss them as irrelevant. Going beyond the linear regime is challenging in the lab, and one might have to look towards astrophysics and cosmology of the early universe instead.  Finally, many interesting features of quantum field theory could be explored in the low-energy regime that may not necessarily be specific to gravity.

The Celestial Holography conjecture posits the existence of a codimension two theory whose correlators compute the S-matrix in a conformal primary basis. Although resembling a CFT in several respects, the intrinsic definition of this proposed dual theory remains elusive. In this talk, I will discuss a conjecture suggesting that Celestial CFT (CCFT) is related to a dimensionally reduced CFT on the Lorentzian cylinder and present some concrete examples of celestial amplitudes constructed in this way.

Covariant loop quantum gravity, commonly referred to as the spinfoam model, provides a regularization for the path integral formalism of quantum gravity. A 4-dimensional Lorentzian spinfoam model with a non-zero cosmological constant has been developed based on quantum SL(2,C) Chern-Simons theory on a graph-complement three-manifold, combined with loop quantum gravity techniques. In this talk, I will give an overview of this spinfoam model and highlight its inviting properties, namely (1) that it yields finite spinfoam amplitude for any spinfoam graph, (2) that it is consistent with general relativity with a non-zero cosmological constant at its classical regime and (3) that there exists a concrete, feasible and computable framework to calculate physical quantities and quantum corrections through stationary phase analysis. I will also discuss recent advancements in this spinfoam model and explore its potential applications.

Hawking’s seminal result, that black holes behave as black bodies with a non-vanishing temperature, suggests that black holes should evaporate. However, Hawking’s derivation is incomplete, as it neglects the backreaction between radiation and geometry. In this talk, we will present a novel approach to black hole perturbation theory that incorporates backreaction and is valid to arbitrary order. The applications to the physics of evaporating black holes is discussed, and we explore potential experimental implications. The intention is to eventually derive corrections to semi-classical computations in the literature and to determine the fate of evaporating black holes.

The study of symmetries at null infinity and their connection with soft theorems via Ward identities has been the subject of intense research over the past decade. The organization of the symmetries in a clear - geometric - structure that reflects the subleading infrared effects has led to numerous interesting results, in particular the emergence of the Lw_{1+\infty} algebra of symmetries for gravity. In this talk I will review recent results on an adaptation of Stueckelberg's procedure to extend phase spaces at null infinity, by which gauge symmetry generators are promoted to dynamical degrees of freedom, containing the so-called edge modes. This formalization allows us to obtain charges corresponding to the subleading soft theorems at all orders, and to construct a hierarchy of closed subalgebras that satisfy simple recursion relations. I will show the example of this construction in Yang-Mills theory, and comment on the charge algebra obtained. Finally, I will discuss the application of this construction to gravity, as well as some preliminary results and future directions.

Emergent Modified Gravity (EMG) is a post-Einsteinian theory of canonical gravity. In this formulation, modified constraints are required to preserve an algebra of hypersurface deformation form and will in general imply modified structure functions. This procedure leads to the conclusion that spacetime is an emergent object with a nontrivial dependence on the gravitational phase space variables through the modified structure functions. Consistency conditions are imposed on the modified constraints and the emergent spacetime metric to ensure general covariance. The resulting modifications allowed by EMG go beyond those obtained from adding higher curvature terms and can result in nonpolynomial dependencies on extrinsic curvature components. In this talk, we discuss how a particular interpretation of such modifications as holonomy terms makes it possible to use EMG as a covariant framework for effective (loop) quantum gravity. We then focus on dynamical solutions of the spherically symmetric model which include nonsingular black holes, new effects to gravitational collapse, and MOND-like effects at intermediate scales.

What does it mean to specify a subregion in a diffeomorphism invariant fashion? This subtle question lies at the heart of many deep problems in quantum gravity. In this talk, we will explore a program of research aimed at answering this question. The two principal characters of the presentation are the extended phase space and the crossed product algebra. The former furnishes a symplectic structure which properly accounts for all of the degrees of freedom necessary to invariantly specify a subregion in gauge theory and gravity, while the latter serves as a quantization of this space into an operator algebra which formalizes the observables of the associated quantum theory. The extended phase space and the crossed product were originally motivated by the problems of the non-invariance/non-integrability of symmetry actions in naive subregion phase spaces, and the non-factorizability/divergence of entanglement entropy in naive subregion operator algebras. The introduction of these structures resolves these issues, while the correspondence between them unifies these resolutions. To illustrate the power of our framework, we demonstrate how the modular crossed product of semiclassical quantum gravity can be reproduced via this approach. We then provide some remarks on how this construction may be augmented in the non-perturbative regime, leading to the notion of a `fuzzy subregion'. We conclude with remarks on currently ongoing and future work, which includes applications to asymptotic and corner symmetries, quantum reference frames, generalized entropy, and the definition of quantum diamonds.

The Ryu-Takayanagi (RT) formula was originally introduced to compute the entropy of holographic boundary conformal field theories. In this talk, I will show how this formula can also be understood as the entropy of an algebra of bulk gravitational observables. Specifically, I will demonstrate that any Euclidean gravitational path integral, when it satisfies a simple set of properties, defines Hilbert spaces associated with closed codimension-2 asymptotic boundaries, along with type I von Neumann algebras of bulk observables acting on these spaces. I will further explain how the path integral naturally defines entropies on these algebras, and how an interesting quantization property leads to a standard state-counting interpretation. Finally, I will show that in the appropriate semiclassical limits, these entropies are computed via the RT formula, thereby providing a bulk Hilbert space interpretation of the RT entropy.