Quantum Gravity

TBA In the framework set by the AdS/MERA conjecture, we investigate a generalisation of the Tensor Network description of bulk geometry in the language of Group Field Theories, a promising convergence of insights and results from Matrix Models, Loop Quantum Gravity and simplicial approaches. We establish a first dictionary between Group Field Theory and Tensor Network states. With such a dictionary at hand, we target the calculation of the Ryu-Takayanagi formula recently derived for Random Tensor Networks in the quantum gravity formalism.

In this talk I will discuss issues and possibilities to outline Quantum Gravity Phenomenology using cosmological and astrophysical data. After a brief review on some formal aspect of the problem I will focus on the analysis of in-vacuo dispersion features for GRB (gamma-ray-burst) neutrinos of energy in the range of 100 TeV, and for GRB photons with energy in the range of 10 GeV. I will introduce a strategy of data analysis which has the advantage of being applicable to several alternative possibilities for the laws of propagation of neutrinos and other particles in a quantum spacetime. Far from being conclusive, the results to be shown should nonetheless motivate a vigorous program of investigation following the methodology of multi-messenger astronomy.

In this talk, I will show that light cones in MInkowski spacetime are a beautiful analoue of black hole horizons in curved spacetime. To do so, I will prove the analogue of the four laws of black hole thermodynamics in this setting. This is what we called light cone thermodynamics. More precisely, I will consider null surfaces defined by the out-going and in-falling wave fronts emanating from and arriving at a sphere in Minkowski spacetime. Such null surfaces, made of pieces of light cones, are bifurcate conformal Killing horizons for suitable conformally stationary observers. They can be extremal and non-extremal depending on the radius of the shining sphere. Such conformal Killing horizons have a constant light cone (conformal) temperature, given by the standard expression in terms of the surface gravity. Considering exchanges of conformally invariant energy across the conformal horizon, one can prove, in perturbation theory, a first law where entropy changes are given by 1/4 of the changes of the area of the bifurcate surface in Planck units. In the extremal case they become light cones associated with a single event; these have vanishing temperature as well as vanishing entropy. I will conclude with possible generalisations and applications of such results.

Compatibility of asymptotic safety with UV-completions of matter theories may constrain the underlying microscopic dynamics of quantum gravity. Within truncated RG-flows, a weak-gravity bound originates from the loss of quantum scale-invariance in the matter system. Further constraints could arise when linking Planck-scale to electroweak-scale dynamics. Within the constrained region, gravitationally induced scale-invariance could UV-complete the Standard Model, and moreover explain free parameters such as fermion masses and gauge couplings.

The SYK model and its variants are a new class of large N conformal field theories. In this talk, we solve SYK, computing all connected correlation functions. Our techniques and results for summing all leading large N Feynman diagrams are applicable to a significantly broader class of theories. 

The Hilbert space of a theory with diffeomorphism symmetry does not factorize into spatial subregions due to gauge constraints. This presents a challenge for defining a notion of entanglement entropy associated with a subregion in these theories. In this talk, I will describe the extended phase space method of Donnelly and Freidel for handling this nonfactorization. It involves introducing edge modes living at the boundary of the subregion, whose purpose is to restore the diffeomorphism invariance that was broken by the subregion's presence. These edge modes are then expected to contribute to the subregion's entanglement entropy. I will further discuss the relevance of the edge mode entanglement to the entropy of black holes, where it may provide a statistical interpretation of the Wald entropy within the low energy effective description.

Recently it was porposed by Hawking, Perry and Strominger that an infinite number of asymptotic charges may play a role in the decription of black hole entropy. With this context in mind we review the classical definition of surface charges in 3+1 gravity (and electromagnetism) from a slighly different framework by using the tetrad-connection variables. The general derivation follows the canonical covariant symplectic formalism in the language of forms. Applications to 3+1 and 2+1 charged and rotating black hole families are briefly discussed as a check. For exact (global) symmetries it is shown to be explicitly equivalent with the 'invariant' symplectic method. Extension to Lovelock gravity are shwon. As an application the entropy expression found by Myers and Jacobson is recovered. [based on arXiv:1703.10120]

There is a growing list of examples where soft factorization theorems in scattering amplitudes can be understood as Ward identities of asymptotic charges. I will review some of these, with emphasis on cases that are not associated to usual conservation laws: leading scalar, subleading photon and sub-subleading graviton soft theorems.

We consider classical, pure Yang-Mills theory in a box. We show how a set of static electric fields that solve the theory in an adiabatic limit correspond to geodesic motion on the space of vacua, equipped with a particular Riemannian metric that we identify. The vacua are generated by spontaneously broken global gauge symmetries, leading to an infinite number of conserved momenta of the geodesic motion. We show that these correspond to the soft multipole charges of Yang-Mills theory.

Quantum effects render black holes unstable. In addition to Hawking radiation, which leads to the prediction of a long lifetime, there is the possibility of quantum tunneling of the black hole geometry itself. A robust possibility for treating the quantum tunneling of a spacetime geometry is through a complex path integral and Picard-Lefschetz theory. I will illustrate the semiclassical approximation of complex path integrals using these techniques with an analytically solvable 1D quantum potential—the inverse square barrier—and describe the setup of the calculation for spherically symmetric black holes. While the black hole calculation is incomplete, I will be able to describe a surprising extension of this setup to the more astrophysical rotating Kerr black hole.

Calculating the path integral over all causal sets will take a lot of computing power, and requires a way to suppress non-manifold like causal sets. To work towards these goals we can start by taking the path integral over a restricted class of causal sets, the 2d orders. Using these have found a phase transition and been able to study the Hartle-Hawking wave function in causal sets. In this talk I will present these recent results (arXiv:1410.8775 and arXiv:1706.06432), and some preliminary data exploring how the behavior of the 2d orders is influenced by coupling them to an Ising model.

Causal set quantum gravity, computational methods Series

The Cactus High Performance Computing (HPC) Framework was designed to
facilitate the development of software to simulate astrophysically realistic
inspiral and merger of binary black holes and neutron stars.  A major part of the motivation for
its design was the US Binary Black Hole Grand Challenge in the 1990s, which
was an alliance of hundreds of scientists, all attempting to collaborate on
the same code base.  In order to handle such a large, diverse collaboration,
the design ended up being extremely general and versatile, able to support
virtually any sort of scientific computation.

I have developed an extensive software suite within the Cactus Framework for
doing large scale computations in discrete quantum gravity, using Causal Sets,
and also spin networks in Loop Quantum Gravity.  Recently, evidence is
emerging that ideas from discrete quantum gravity, and consequently this
software, may have much broader application in areas of Data Science,
including social science, computational neuroscience, and drug design.