Quantum Gravity

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

The event horizon of a dynamical black hole is generically a non-smooth hypersurface. I shall describe the types of non-smooth structure that can arise on a horizon that is smooth at late time. This includes creases, corners and caustic points. I shall discuss ``perestroikas'' of these structures, in which they undergo a qualitative change at an instant of time. A crease perestroika gives an exact local description of the event horizon near the ``instant of merger'' of a generic black hole merger. Other crease perestroikas describe horizon nucleation or collapse of a hole in a toroidal horizon. I shall discuss the possibility that creases contribute to black hole entropy, and the implications of non-smoothness for higher derivative terms in black hole entropy. This talk is based on joint work with Maxime Gadioux.

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Zoom link: https://pitp.zoom.us/j/98839294408?pwd=cytNYThQaDV4Y2lob1REY0NyaTJNUT09

With the main purpose of identifying the existence of gravitational radiation at infinity (scri), a novel approach to the asymptotic structure of spacetime is presented, focusing mainly in cases with non-negative cosmological constant. The basic idea is to consider the strength of tidal forces experienced by scri. To that end I will introduce the asymptotic (radiant) super-momentum, a causal vector defined at scri with remarkable properties that, in particular, provides an innovative characterization of gravitational radiation valid for the general case with Λ ≥ 0 (and which has been proven to be equivalent when Λ = 0 to the standard one based on the News tensor). This analysis is also shown to be supported by the initial- (or final-) value Cauchy-type problem defined at scri. The implications are discussed in some detail. The geometric structure of scri, and of its cuts, is clarified. The question of whether or not a News tensor can be defined in the presence of a positive cosmological constant is addressed. Several definitions of asymptotic symmetries are presented. Conserved charges that may detect gravitational radiation are exhibited. Balance laws that might be useful as diagnostic tools to test the accuracy of model waveforms discussed. An interpretation of the Geroch `rho' tensor is found. The whole thing will be complemented with a series of illustrative examples based on exact solutions. In particular we will see that exact solutions with black holes will be radiative if, and only if, they are accelerated.

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Zoom link https://pitp.zoom.us/j/96816406686?pwd=eGZINlo2R0d1YkZMRGhackRNMzBVUT09

With the main purpose of identifying the existence of gravitational radiation at infinity (scri), a novel approach to the asymptotic structure of spacetime is presented, focusing mainly in cases with non-negative cosmological constant. The basic idea is to consider the strength of tidal forces experienced by scri. To that end I will introduce the asymptotic (radiant) super-momentum, a causal vector defined at scri with remarkable properties that, in particular, provides an innovative characterization of gravitational radiation valid for the general case with Λ ≥ 0 (and which has been proven to be equivalent when Λ = 0 to the standard one based on the News tensor). This analysis is also shown to be supported by the initial- (or final-) value Cauchy-type problem defined at scri. The implications are discussed in some detail. The geometric structure of scri, and of its cuts, is clarified. The question of whether or not a News tensor can be defined in the presence of a positive cosmological constant is addressed. Several definitions of asymptotic symmetries are presented. Conserved charges that may detect gravitational radiation are exhibited. Balance laws that might be useful as diagnostic tools to test the accuracy of model waveforms discussed. An interpretation of the Geroch `rho' tensor is found. The whole thing will be complemented with a series of illustrative examples based on exact solutions. In particular we will see that exact solutions with black holes will be radiative if, and only if, they are accelerated.

Zoom link: https://pitp.zoom.us/j/95879544523?pwd=MFl5UEtUZ0hUcU1hNk1SZ2R4MThxUT09

66 - It has been proposed that the exponential decay and subsequent power law saturation of out-of-time-order correlation functions can be universally described by collective 'scramblon' modes. We develop this idea from a path integral perspective in several examples, thereby establishing a general formalism. After reformulating previous work on the Schwarzian theory and identity conformal blocks in two-dimensional CFTs relevant for systems in the infinite coupling limit with maximal quantum Lyapunov exponent, we focus on theories with sub-maximal chaos: we study the large-q limit of the SYK quantum dot and chain, both of which are amenable to analytical treatment at finite coupling. In both cases we identify the relevant scramblon modes, derive their effective action, and find bilocal vertex functions, thus constructing an effective description of chaos. The final results can be matched in detail to stringy corrections to the gravitational eikonal S-matrix in holographic CFTs, including a stringy Regge trajectory, bulk to boundary propagators, and multi-string effects that are unexplored holographically.

I will argue that a fruitful strategy to make progress in quantum gravity is to connect distinct approaches and transfer methods and ideas from one approach to another. As a concrete example, I will explain recent results in causal-set quantum gravity. The first, namely the construction of a higher-order curvature operator in causal sets, is motivated by the idea to use causal sets as a Lorentzian regularization of the gravitational path integral, in which one can search for asymptotic safety. The second, namely an upper bound on the mass of scalars is inspired by the "matter matters" program in asymptotically safe quantum gravity, in which observational tests of quantum gravity are based on gravity's interplay with matter. I will argue that a similar program for causal sets can provide new, observationally motivated constraints on causal set quantum gravity.To provide background and motivation for these results, I'll provide brief and pedagogical introductions into the key features and key open challenges of both asymptotically safe quantum gravity as well as causal set quantum gravity.

Zoom Link: https://pitp.zoom.us/j/99855484685?pwd=M0IvOFk1OWNCdVlZVDdkUFQ4MzZKUT09