Quantum Gravity

We will explore the connection between Celestial and Euclidean Anti-de Sitter (EAdS) holography in the massive scalar case. Specifically, exploiting the so-called hyperbolic foliation of Minkowski space-time, we will show that each contribution to massive Celestial correlators can be reformulated as a linear combination of contributions to corresponding massive Witten correlators in EAdS. This result will be demonstrated explicitly both for contact diagrams and for the four-point particle exchange diagram, and it extends to all orders in perturbation theory by leveraging the bootstrapping properties of the Celestial CFT (CCFT).  Within this framework, the Kantorovic-Lebedev transform plays a central role, which will be introduced at the end of the talk. This transform will allow us to make broader considerations regarding non-perturbative properties of a CCFT. 

Abstract:  In relativity, the geometry of the light cones determines the causal structure of spacetime. Under the influence of gravity, the light cones bend and curve. A previously expanding light cone can fall back into itself. In this way, the causal structure becomes a dynamical aspect of spacetime. How do we understand this link between gravity, geometry and causality at the quantum level? Is there a quantum light cone geometry? In my talk, I will argue that the answer to this problem is crucial for making progress in quantum gravity. It is, in fact, a problem that is shared among different approaches, from holography, to celestial amplitudes and loop quantum gravity. In my presentation, I report on three new results on this frontier. First, I provide a non-perturbative characterization of impulsive gravitational null initial data for tetradic gravity on a light cone. Second, the description is taken to the quantum level. Third, an immediate physical implication is found: in the model, the Planck luminosity separates the eigenvalues of the radiated power. Below the Planck power, the spectrum of the radiated power is discrete. Above the Planck power, the spectrum is continuous and the resulting physical states contain caustics that can spoil the semi-classical limit.  The talk is based on arXiv:2402.12578, arXiv:2401.17491, arXiv:2104.05803.

Some of the most fundamental challenges in quantum gravity involve determining how to take the continuum limit of the underlying regularized theory and how to preserve the causal structure of space-time. Several approaches to quantum gravity attempt to address these questions, but the technical challenges are substantial.

In this talk, we present a novel approach to a lattice-regularized theory of quantum gravity, using techniques from standard lattice quantum field theories to overcome these challenges. Our approach is inspired by quantum geometrodynamics, the earliest attempt at quantizing gravity. While the original approach suffered from the usual shortcomings pertaining to the multiplication of distributions and consequently failed, we propose a novel lattice regularization that is especially well suited for studying the continuum limit. First, we examine the lattice corrections to the theory and quantize these lattice theories in a manner that ensures the manifest causal structure of space-time. Next, we discuss the constructions involved in obtaining a well-defined continuum limit and explain how our approach can overcome some conceptually unappealing aspects.

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Asymptotically safe quantum gravity might provide a unified description of the fundamental dynamics of quantum gravity and matter. The realization of asymptotic safety, i.e., of scale symmetry at high energies, constraints the possible interactions and dynamics of a system. In this talk, I will first introduce the scenario of asymptotic safety for gravity with matter, and explain how it can be explored using functional methods. I will then emphasize, how the constraints on the microscopic dynamics of matter arising from quantum scale symmetry can turn into constraints on the gravitational dynamics, both by exploring the asymptotically safe fixed-point structure, and by exploring resulting infrared physics.

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A Planck scale inflationary era—in a quantum gravity theory predicting discreteness of quantum geometry at the fundamental scale—produces the scale invariant spectrum of inhomogeneities with very small tensor-to-scalar ratio of perturbations and a hot big bang leading to a natural dark matter genesis scenario. In this talk I evoke the possibility that some of the major puzzles in cosmology could have an explanation rooted in quantum gravity.

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I will review the "gyroscopic gravitational memory”, the permanent effect of gravitational waves on freely-falling gyroscopes far from the source of gravitational radiation. Then, I will compute the effect created by binary systems in the post-Newtonian approximation. The discussion naturally involves the helicity of gravitational waves and gravitational electric-magnetic duality.

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The concept of symmetries is crucial in our comprehension of modern theoretical physics. The Corner Proposal introduces a novel framework where symmetries are reinstated as foundational principles in our understanding of gravity. This aims to describe gravity using a language that is more adapted to quantization. In this presentation, I will start by providing an overview of the essential results leading to the main ideas the proposal. This will then allow me to state the proposal in the general case to then specialize to 1+1 dimensional gravity.

Finally, I will present elements of our recent research applying the proposal to the case of 1+1 dimensional gravity. I will demonstrate the framework's promising potential by calculating the entanglement entropy between two spatial regions—a significant challenge in quantum gravity. The result is the 1+1 dimensional equivalent of the well-established Bekenstein-Hawking area law governing the entropy of gravitational systems with the expected behavior of the quantum corrections.

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Correlation functions are ubiquitous in quantum field theory, but their use in quantum gravity beyond perturbative and asymptotically flat regimes has been limited, due to difficulties with diffeomorphism invariance and the dynamical nature of geometry. We address these challenges in the context of nonperturbative quantum gravity, motivated by the goal of computing geometric correlators from first principles, as a possible window to early-universe cosmology. I will report on recent work in 2D Lorentzian quantum gravity, formulated in terms of causal dynamical triangulations, which demonstrates the feasibility of constructing and measuring manifestly diffeomorphism-invariant curvature correlators. I will discuss some unusual features of the connected correlators and new results on their behaviour in two dimensions, obtained with the help of Monte Carlo simulations.

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At the classical level, one can restrict a spherically symmetric model to the corresponding LTB sector by requiring that a so-called LTB condition is satisfied. In this talk we will discuss how this can be generalised in the context of effective models containing quantum gravity inspired modifications of  the classical theory in the form of polymerisations. The formalism presented allows us to consider more general polymerisations than in previous work in the literature. Applications of this framework are then considered, focusing on a particular class of models that have the property that the effective dynamics is completely decoupled along the radial direction. Examples of effective models that fall into this class are discussed and their physical properties are compared with existing models in the literature.

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I will review recent progress in the asymptotic safety approach to quantum gravity. This includes the computation of momentum-dependent graviton correlation functions, the structure of the Standard Model with asymptotically safe gravity, and the recent first computation directly in space-times with Lorentzian signatures via the spectral function of the graviton. Overall, I will display the progress towards the computation of the quantum effective action which encapsulates effective field theory in the IR limit and the asymptotic safety regime in the UV limit.

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We show that the Ryu-Takayanagi (RT) formula, originally introduced to compute the entropy of a holographic boundary CFT, can be interpreted as entropy of an algebra of bulk gravitational observables. In particular, we show that any Euclidean gravitational path integral satisfying a simple and familiar set of axioms defines type I von Neumann algebras of bulk observables acting on closed codimension-2 asymptotic boundaries. The entropies associated to these algebras, defined via the gravitational path integral, can be written in terms of standard density matrices and standard Hilbert space traces, and in appropriate semiclassical limits are computed by the RT formula with quantum corrections. Our work thus provides a bulk state-counting interpretation of the Ryu-Takayanagi entropy. Since our axioms do not severely constrain UV bulk structures, they may be expected to hold equally well for successful formulations of string field theory, spin-foam models, or any other approach to constructing a UV-complete theory of gravity.

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