Quantum Gravity

We compute the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. These are Euclidean wormholes, which smoothly interpolate between two asymptotically Euclidean AdS3 regions with torus boundary. From our results we obtain the spectral correlations between BTZ black hole microstates near threshold, as well as extract the spectral form factor at fixed momentum, which has linear growth in time with small fluctuations around it. The low-energy limit of these correlations is precisely that of a double-scaled random matrix ensemble with Virasoro symmetry. Our findings suggest that if pure three-dimensional gravity has a holographic dual, then the dual is an ensemble which generalizes random matrix theory.

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."

Harlow and Hayden [arXiv:1301.4504] argued that distilling information out of Hawking radiation is computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. I will trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by tensor network models, I will present a conjecture that relates the computational hardness of distilling information to geometric features of the wormhole - specifically to the exponential of the difference in generalized entropies between the two non-minimal quantum extremal surfaces that constitute the obstruction. Due to its shape, this obstruction was dubbed "Python's Lunch", in analogy to the reptile's postprandial bulge.

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.

When Alice shares thermofield double with Bob, her time evolution can make the wormhole grow. We identify different kinds of operations Alice can do as being responsible for the growth of different parts of spacetime and see how it fits together with subregion duality. With this, we give a quantum circuit interpretation of evaporating black hole geometry. We make an analogy between the appearance of island for evaporating black hole and the transition from two-sided to one-sided black hole in the familiar example of perturbed thermofield double. If Alice perturbs thermofield double and waits for scrambling time, she will have a one-sided black hole with interior of her own. We argue that by similar mechanism the radiation gets access to the interior (island forms) after Page time. The growth of the island happens as a result of the constant transitions from two-sided to one-sided black holes.

Hosted By: Stanford University  Footage Courtesy: Simons Foundation for Mathematics and Physical Sciences

The covariant (spinfoam) formulation of loop gravity is a tentative physical quantum theory of gravity with well defined transition amplitudes.  I give my current understanding of the state of the art in this research direction, the issues that are open and need to be explored, and the current attempts to use the theory to compute quantum effects in the early universe and in black hole physics.

It is well-known that quantum groups are relevant to describe the quantum regime of 3d gravity. They encode a deformation of the gauge symmetries (Lorentz symmetries) parametrized by the value of the cosmological constant. They appear as some kind of regularization either through the quantization of the Chern-Simons formulation (Fock-Rosly formulation/combinatorial quantization, path integral quantization) or the state sum approach (Turaev-Viro model). Such deformation might be perplexing from a classical picture since the action is defined in terms of plain/undeformed gauge symmetry. I would like to present here a novel way to derive/justify such quantum group deformation, starting from the classical action.

In the 1980’s, work by Coleman and by Giddings and Strominger linked the physics of spacetime wormholes to ‘baby universes’ and an ensemble of theories. We revisit such ideas, using features associated with a negative cosmological constant and asymptotically AdS boundaries to strengthen the results, introduce a change in perspective, and connect with recent replica wormhole discussions of the Page curve. A key new feature is an emphasis on the role of null states. We explore this structure in detail in simple topological models of the bulk that allow us to compute the full spectrum of associated boundary theories. We also argue that similar properties must hold in any consistent gravitational path integral.

Hosted By: Stanford University  Footage Courtesy: Simons Foundation for Mathematics and Physical Sciences