Quantum Gravity

We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

In this talk, I will revisit the calculation of infinite-dimensional symmetries that emerge in the vicinity of isolated horizons. In particular, I will focus my attention on extremal black holes, for which the isometry algebra that preserves a sensible set of asymptotic boundary conditions at the horizon strictly includes the BMS algebra. The conserved charges that correspond to this BMS sector, however, reduce to those of superrotation, generating only two copies of Witt algebra. For more general horizon isometries, in contrast, the charge algebra does include both Witt and supertranslations, being similar to BMS but s.str. differing from it. I will also show how this is extended to the case of black holes in the Einstein-Yang-Mills case, where a loop algebra associated to the gauge group is found to emerge at the horizon.

A basic calculation in QFT is the construction of the Yukawa potential from a tree-level scattering amplitude. In the massless limit, this reproduces the 1/r potential. For gravity, scattering mediated by a massless graviton is thus consistent with the Newtonian potential.

In de Sitter spacetime, the cosmological constant gives rise to a mass-like term in the graviton propagator. This raises the question what the classical potential looks like when taking into account curvature effects.

In this talk, I will introduce an operator-based formalism to compute scattering amplitudes in curved spacetime, and I will show how to construct the Newtonian potential in a dS background. Remarkably, the potential gives rise to an additional repulsive force, and encodes the de Sitter horizon in a novel and non-trivial way.

Over the past decades, the asymptotic safety scenario has matured into a viable contender for a consistent theory of quantum gravity. However, the pressing question of unitarity is far from being settled. I will present important steps towards tackling this issue and show the first direct computation of the graviton spectral function in asymptotically safe quantum gravity with a novel Lorentzian renormalisation group approach. We find a positive graviton spectral function, showing a massless one-graviton peak and a multi-graviton continuum with an asymptotically safe scaling for large spectral values. For small spectral values, the effective field theory result is approached. I will indicate consequences for scattering amplitudes and unitarity.

We expect certain universal results in classical gravity to come unaltered from a quantum theory of gravity. In this talk, I will firstly discuss new ideas on this topic, and the latest understanding we have on this, in an accessible way. After that, I will focus on local symmetries in gravity, and obtain the most general off-shell algebra of diffeomorphisms that acts non-trivially at corners, where gauge charges are supported. Noether charges in Einstein gravity are then shown to generate a faithful representation of this algebra. After pausing and reviewing the covariant phase space formulation, explaining the questions and issues our community faced in successfully applying it to gravity, I will show how a careful treatment of embeddings allows us to establish a field space where Noether charges act canonically via Poisson bracket. This solves a longstanding puzzle in this field, opening doors to new promising investigations. I will conclude by mentioning them and commenting on how new proposals might shed light on old unanswered questions in quantum gravity.

Zoom Link: https://pitp.zoom.us/j/96552295909?pwd=cFZwcGxLdWlaWWhRS21RMExUd1RjQT09

I study the dynamics of a gyroscope far from an isolated source of gravitational waves. With respect to a local frame 'tied to the distant stars', the gyroscope precesses when gravitational waves cross its path, resulting in a net `orientation memory', carrying information on the gravitational wave profile. I show that the precession rate is given by the so-called "dual covariant mass aspect", providing a celestially local measurement protocol for this quantity. Moreover, I show that the net memory effect can be derived from the flux-balance equations for superrotation charges in the "generalized BMS" algebra. Finally, I show how the spin memory effect à la Pasterski et al. is reproduced as a special case.

Conformal field theories have played an important role in understanding the origin of gravitational entropy, as the Cardy formula accounts for the entropy of three-dimensional BTZ black holes or black holes with an AdS3 near-horizon region. More recently, Cardy-type formulas have also been derived for different field theories, such as warped conformal field theories, which are two-dimensional field theories invariant under chiral scaling symmetry.

In this talk I discuss a particular class of three-dimensional spacetimes, dubbed warped flat spaces. I will present their geometric and thermodynamic properties, focusing on their causal structure. I will explain how their entropy can be accounted for through a dual description in terms of a warped conformal field theory.

For quantum gravity states associated to open spin network graphs, we study how the boundary (the set of open edges, which carries spin degrees of freedom) is affected by the bulk, specifically by its combinatorial structure and by the quantum correlations among the intertwiners. In particular, we determine under which conditions certain classes of quantum gravity states map bulk degrees of freedom into boundary ones isometrically (which is a necessary condition for holography). We then look at the entanglement entropy of the boundary and recover, for slightly entangled intertwiners, the Ryu-Takayanagi formula with corrections induced by the entanglement entropy of the bulk state. We also show that the presence of a region with highly entangled intertwiners deforms the minimal-area surface, which is prevented from entering that region when the entanglement entropy of the latter exceeds a certain bound, a mechanism which thus leads to the rise of a black hole-like region in the bulk.

Zoom Link: https://pitp.zoom.us/j/96356007543?pwd=U2VrRlhyOThMODdMYllDMnB6VjlZQT09

The main feature of tensor models is their melonic large N limit, leading to applications ranging from random geometry and quantum gravity to  many-body quantum mechanics and conformal field theories. However, this melonic limit is lacking for tensor models with ordinary representations of O(N) or Sp(N). We demonstrate that random tensors with sextic interaction transforming under rank-5 irreducible representations of O(N) have a melonic large N limit. This extends the recent proof obtained for rank-3 models with quartic interaction. After giving an introduction to random tensors, I will present the main ideas of our proof relying on recursive bounds derived from a detailed combinatorial analysis of the Feynman graphs.

Zoom Link: https://pitp.zoom.us/j/94691275506?pwd=RGFaN0NZR0FScFdOTXFzeFVXaXUvUT09

This talk focuses on the semiclassical behavior of the spinfoam quantum gravity in 4 dimensions. There has been long-standing confusion, known as the flatness problem, about whether the curved geometry exists in the semiclassical regime of the spinfoam amplitude. The confusion is resolved by the present work. By numerical computations, we explicitly find curved Regge geometries from the large-j Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam amplitudes on triangulations. These curved geometries are with small deficit angles and relate to the complex critical points of the amplitude. The dominant contribution from the curved geometry to the spinfoam amplitude is proportional to e^{i I}, where I is the Regge action of the geometry plus corrections of higher order in curvature. As a result, the spinfoam amplitude reduces to an integral over Regge geometries weighted by e^{i I} in the semiclassical regime.  As a byproduct, our result also provides a mechanism to relax the cosine problem in the spinfoam model. Our results provide important evidence supporting the semiclassical consistency of the spinfoam quantum gravity.

Zoom Link: https://pitp.zoom.us/j/93699343757?pwd=RnpFeitaTU5qTktzNjlXQW45K1gvQT09

Quantum groups are the proper tool to describe quantum gravity in three dimensions. Several arguments suggest that 2-groups should be used to formulate four dimensional quantum gravity. I will review these motivations and will discuss in particular how 2-groups can be used to extend the definition of a phase space associated to a triangulation or to modify the notion of group field theory to generate topological models. I will also highlight how the kappa Poincaré deformation arises in the 2-group context.

Time at the Planck scale is an unexplored physical regime. It is widely believed that probing Planck time will remain for long an impossible task. Yet, we propose an experiment to test the discreteness of time at the Planck scale and show that it is not far removed from current technological capabilities.