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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