Quantum Gravity

In my talk, I'll review the key idea underlying asymptotically safe quantum gravity, before giving an overview of the current status and open questions. I'll then spotlight three challenges. The first challenge is how to test quantum gravity and I'll advocate that by linking quantum gravity to particle physics and cosmology, we can probe quantum gravity at all scales. The second challenge is how to connect to other ideas about quantum spacetime and I'll discuss effective asymptotic safety as a way to link to, e.g., string theory. The third challenge is the status of global symmetries and I'll discuss what we know about the preservation of global symmetries in asymptotic safety and what this implies for a broader perspective on the question. --- The presenter will be joining via Zoom for this talk.

The Celestial Holography program encompasses recent efforts to understand the flat space hologram in terms of a CFT living on the celestial sphere. A key development instigating these efforts came from understanding how soft limits of scattering encode infinite dimensional symmetry enhancements corresponding to the asymptotic symmetry group of the bulk spacetime. Historically, the construction of the bulk-boundary dual pair has followed bottom up approach matching symmetries on both sides. Recently, however, there has been exciting progress in formulating top down descriptions using insights from twisted holography. We review salient aspects of the celestial construction, the status of the dictionary, and active research directions.

At first sight, it seems that almost any QFT, seen as a low-energy effective field theory (EFT), can be coupled to gravity -- simply add an Einstein-Hilbert term, change all derivatives by covariant ones, and you're done. However, a growing body of evidence coming from String Theory compactifications, general properties of black hole evaporation, and rigorous results in holography, suggests that the opposite is true. We can work out the hidden constraints that quantum gravity consistency imposes in the matter sector systematically, an approach that receives the colourful name of "The Swampland Program". I will briefly review the program, its motivation, current results, and long-term goals.

I will review implications of the AdS/CFT correspondence for quantum gravity, paying particular attention to holographic RG flows and the processing of information. Deformed hyperbolic geometries correspond to boundary field theory RG flows. Conversely, as I will exemplify using the recent approach of discrete holography, boundary RG flows may be used to reconstruct the bulk spacetime, for instance via tensor networks. I will discuss recent approaches towards including gravity dynamics into this reconstruction process. --- The presenter will be joining via Zoom for this talk.

I will briefly review the key concepts underlying the Effective Field Theory of General Relativity, and give a couple of examples of how it works. Then I will describe seven lessons which can be extracted from the theory. Finally I discuss some of the limitations of the EFT framework.

 

Motivated by the static patch of de Sitter space, we discuss timelike surfaces in general relativity and the initial boundary value problem. We consider the Dirichlet problem and a conformal version thereof. Time permitting we discuss some ideas in lower dimensions.

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Zoom link https://pitp.zoom.us/j/98357788662?pwd=b3lHS3Q3T2xkNm53SkR3QVVvTGJMdz09

Building on the fact that quantum uncertainty is a dynamical degree of freedom in itself in quantum mechanics, I will start with the remark that its evolution can provide a notion of intrinsic clock. To illustrate the non-triviality of this idea, we’ll check the dynamics of the uncertainty if gravitizing quantum mechanics into a non-linear Schrödinger equation, and will see that it (surprisingly?) follows the same trajectories as planetary orbits. A third thread will come from the black hole mini-superspace in general relativity. We will see that, assuming that the quantization preserves all the symmetries of the theory, universal quantum gravity corrections can also be written as a non-linear Schrödinger equation, leading to a non-trivial evolution of the “classicality” of black hole wave-packets along the radial coordinate.

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Zoom link: https://pitp.zoom.us/j/95808416532?pwd=cHJnVXpzdDd3eXdFbUlMamFsMFV3UT09

In classical relativity we usually think of the metric signature as fixed, but quantum cosmology already forces us to consider more general situations such as transitions from Riemannian to Lorentzian signature. I will discuss the less studied phenomenon of an overall "flip" where all metric components change sign simultaneously (e.g., from "East Coast" to "West Coast" signature). Such an overall flip can represent saddle point solutions in quantum cosmology, or appear classically in the Plebański formalism or even a slight extension of Einstein--Hilbert gravity. Interestingly, at such a transition the cosmological constant can change both sign and magnitude, with a pure sign change being the most minimalistic proposal. Cosmological solutions transitioning classically between de Sitter and anti de Sitter can be found immediately, and the quantisation of a minisuperspace model turns out to be simpler than in the fixed signature case: in particular, the gravitational action reduces to a pure boundary term. Various other applications and the relation to unimodular gravity are also discussed.

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Zoom link: https://pitp.zoom.us/j/93255772501?pwd=bWhzZUVBOTM2a3QvTGlXVGJ5TlZnUT09

Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. We generalize the Fefferman-Graham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl manifolds. We first introduce the Weyl-ambient metric motivated by the Weyl-Fefferman-Graham (WFG) gauge, which is a generalization of the FG gauge for asymptotically locally AdS (AlAdS) spacetimes. Then, the Weyl-ambient space as a pseudo-Riemannian geometry induces a codimension-2 Weyl geometry. Through the Weyl-ambient construction, we investigate Weyl-covariant quantities on the Weyl manifold and define Weyl-obstruction tensors. We show that Weyl-obstruction tensors appear as poles in the Fefferman-Graham expansion of the AlAdS bulk metric for even boundary dimensions. Under holographic renormalization, we demonstrate that Weyl-obstruction tensors can be used as the building blocks for the Weyl anomaly of the dual quantum field theory.

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Zoom link https://pitp.zoom.us/j/91781363979?pwd=NlhjTVlHTlhMSTcxYnk5eExkTWFqdz09