Quantum Gravity

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.

A burst of gravitational radiation passing through an arrangement of freely falling test masses far from the source will cause a permanent displacement of the masses, called the ''gravitational memory''. It has recently been found that this memory is closely related to the change in the so called ''super-translation'' charge carried by the spacetime, where ''super-translations'' here refer to an unexpected enlargement of the asymptotic symmetries of general relativity beyond the expected asymptotic Poincare-transformations, known already since the work of Bondi et al. in the early 60s (no relation with ‘’supersymmetry''). I will describe these concepts from an intuitive perspective and point out that super-translations, as well as gravitational memory, are a phenomenon that is unique to relativity in 3+1, but not higher, dimensions. I close the talk by explaining the relation between these results and the notion of a ''charge super-selection sector'' in quantum field theories with massless particles such as QED.

[Based on joint work with A. Ishibashi and R. M. Wald]

I will discuss the possibilities to mimic black hole physics in fluid flows. The starting point is an analogy discovered by Unruh between the propagation of sound in a flowing fluid and waves around a black hole. In these analog setups, it is possible to test various black hole effects, and challenge their robustness. In a recent water wave experiment, we have shown how to exploit this analogy to observe superradiant scattering, that is, the amplification of waves by extraction of angular momentum from a rotating flow.

I will talk about the relation between non-local theories and gravity. The main thesis is that non-local field theories naturally induce gravity, even at the classical level. Supporting this idea, I will study bi-local scalar field theories, which involve minimal deviations from locality. We will treat them both, bi-local theories and gravity perturbatively. We will see that bi-local theories encode gravity together with higher spin fields.

I will discuss the role(s) of the Immirzi parameter in Loop Quantum Gravity, insisting on the Poisson algebra formed by Thiemann's complexifier, the volume and the Hamiltonian constraint. In particular, we will see how loop quantum cosmology is a direct quantization of this CVH Poisson algebra and how cosmological evolution amounts to a flow in the Immirzi parameter.