Quantum Gravity

I will discuss the recent Hamiltonian derivation of dual BMS charges at null infinity using the first order formalism.  More generally, I will discuss how this idea can be used to classify asymptotic charges in gravity.

Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. Along this line, a prime question is to find whether gravity is a quantum entity subject to the rules of quantum mechanics. It is fair to say that there are no feasible ideas yet to test the quantum coherent behaviour of gravity directly in a laboratory experiment. Here, I will introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. I will show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. I will provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple correlation measurements between two spins: one embedded in each test mass. Fundamentally, the above entanglement is shown to certify the presence of non-zero off-diagonal terms in the coherent state basis of the gravitational field modes.

I discuss general argument to show that if a physical system can mediate locally the generation of entanglement between two quantum systems, then it itself must be non-classical. Remarkably, the argument does not assume any classical or quantum formalism to describe the mediating physical system: the result follows from general information-theoretic principles. This argument provides a robust and general theoretical basis for recently proposed tests of non-classicality in gravity, based on witnessing gravitationally-induced entanglement in quantum probes.

Renormalisation in curved spacetimes is an involved subject. In contrast to renormalisation in a flat spacetime, the standard momentum representation is not directly available. Nevertheless, the momentum dependence of correlation functions is crucial to deciding whether a theory is unitary and causal. I will discuss how to define a notion of momentum dependence in gravity on a fundamental level. With this at hand, one can discuss an important quantum field theory observable: scattering cross sections. Taking the example of gravity-mediated scalar scattering, I will discuss conditions that a quantum field theory of gravity has to fulfil to have a well-behaved scattering amplitude. These can be satisfied without the introduction of massive higher spin modes as is done in string theory. Finally, I will review the status of first principle calculations of the non-perturbative momentum dependence of quantum gravity correlation functions.

The Raychaudhuri equation predicts the convergence of geodesics and gives rise to the singularity theorems. The quantum Raychaudhuri equation (QRE), on the other hand, shows that quantal trajectories, the quantum equivalent of the geodesics, do not converge and are not associated with any singularity theorems. Furthermore, the QRE gives rise to the quantum corrected Friedmann equation. The quantum correction is dependent on the wavefunction of the perfect fluid whose pressure and density enter the Friedmann equation. We show that for a suitable choice of the wavefunction this term can be interpreted as a small positive cosmological constant.

We will argue that even with semiclassical gravity, it can be shown that a copy of  all the information on a Cauchy slice resides near the boundary of the slice. We will first demonstrate this in asymptotically global AdS, and then in four-dimensional asymptotically flat space. We will then describe a physical protocol that can be used to verify this property at low-energies and within perturbation theory. This property of gravity implies that information about the black-hole interior is always present "outside" the black hole, which leads to a fresh perspective on the information paradox.

References:
1) https://arxiv.org/abs/2002.02448
2) https://arxiv.org/abs/2008.01740

The computation of transition amplitudes in Loop Quantum Gravity is still a hard task, especially without resorting to large-spins approximations. In Marseille we are actively developing a C library (sl2cfoam) to compute Lorentzian EPRL amplitudes with many vertices. We have already applied this tool to obtain interesting results in spinfoam cosmology and on the so-called flatness problem of spinfoam models. I will highlight the main aspects of our software library, describe the current applications and also introduce undergoing developments (Montecarlo over spin space, tensor contractions, GPU offloading) that will greatly enhance the library's speed and capabilities.

Since the seminal work of Penrose, it has been understood that conformal compactifications (or "asymptotic simplicity") is the geometrical framework underlying Bondi-Sachs' description of asymptotically flat space-times as an asymptotic expansion. From this point of view the asymptotic boundary, a.k.a "null-infinity", naturally is a conformal null (i.e degenerate) manifold. In particular, "Weyl rescaling" of null-infinity should be understood as gauge transformations. As far as gravitational waves are concerned, it has been well advertised by Ashtekar that if one work with a fixed representative for the conformal metric, gravitational radiations can be neatly parametrized as a choice of "equivalence class of metric-compatible connections". This nice intrinsic description however amounts to working in a fixed gauge and, what is more, the presence of equivalence class tend to make this point of view tedious to work with.

I will review these well-known facts and show how modern methods in conformal geometry (namely tractor calculus) can be adapted to the degenerate conformal geometry of null-infinity to encode the presence of gravitational waves in a completely geometrical (gauge invariant) way: Ashtekar's (equivalence class of) connections are proved to be in 1-1 correspondence with choices of (genuine) tractor connection, gravitational radiation is invariantly described by the tractor curvature and the degeneracy of gravity vacua correspond to the degeneracy of flat tractor connections. The whole construction is fully geometrical and manifestly conformally invariant."

Using a definition of bulk diff-invariant observables, we go into the bulk of 2d Jackiw-Teitelboim gravity. By mapping the computation to a Schwarzian path integral, we study exact bulk correlation functions and discuss their physical implications. We describe how the black hole thermal atmosphere gets modified by quantum gravitational corrections. Finally, we will discuss how higher topological effects further modify the spectral density and detector response in the Unruh heat bath. 

We introduce a new technique to study the critical point equations of the eprl model. We show that it correctly reproduces the 4-simplex asymptotics, and how to apply it to an arbitrary vertex. We find that for general vertices, the asymptotics can be linked to a Regge action for polytopes, but contain also more general geometries, called conformal twisted geometries. We present explicit examples including the hypercube, and discuss implications.

The full theory of LQG presents enormous challenge to create physical computable models. In this talk we will present the new modern version of Quantum Reduced Loop Gravity. We will show that this framework provide an arena to study the full LQG in a certain limit, where the quantum computations are possible. We will analyze all the major step necessary to build this framework, how is connected with the full theory, its mathematical consistency and the physical intuition behind It.

Quantum-reduced loop gravity is a model of loop quantum gravity, whose characteristic feature is the considerable simplicity of its kinematical structure in comparison with that of full loop quantum gravity. The model therefore provides an accessible testing ground for probing the physical implications of loop quantum gravity. In my talk I will give a brief introduction to quantum-reduced loop gravity, and examine the relation between the quantum-reduced model and full loop quantum gravity. In particular, I will focus on clarifying how the operators of the quantum reduced model are related to those of the full theory. I will show that despite their simplicity, the operators of the quantum-reduced model are simply the operators of the full theory acting on states in the Hilbert space of the quantum-reduced model. In order to pass from the full theory operators to the "reduced" operators, one only has to keep in mind that the states of the quantum-reduced model are labeled with large spins, and discard terms which are of lower than leading order in j.