Quantum Gravity

We develop the reduced phase space quantization of causal diamonds in $2+1$ dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a spacelike topological disk with fixed (induced) boundary metric. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$, i.e., the group of orientation-preserving diffeomorphisms of the circle modulo the projective special linear subgroup. Classically, the states correspond to causal diamonds embedded in $AdS_3$ (or $Mink_3$ if $\Lambda = 0$), with a fixed corner length, that have the topological disk as a Cauchy surface. Because this phase space does not admit a global system of coordinates, a generalization of the standard canonical (coordinate) quantization is required --- in particular, since the configuration space is a homogeneous space for a Lie group, we apply Isham's group-theoretic quantization scheme. The Hilbert space of the associated quantum theory carries an irreducible unitary representation of the $BMS_3$ group, and can be realized by wavefunctions on a coadjoint orbit of Virasoro with labels in irreducible unitary representations of the corresponding little group. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the corner length.

Zoom link:  https://pitp.zoom.us/j/94369372201?pwd=NWNsYno3RmZIWUx0LytWZ09PVDVVQT09

I will discuss several issues related to the computation of Poisson brackets in field theories. I will show that by choosing appropriate functional spaces as configuration manifolds, it is possible to avoid the use of distributions. This is relevant, for instance, in the context of Loop Quantum Gravity, where the basic holonomy/flux variables play a central role. I will illustrate the main ideas by using simple examples based on Sobolev spaces.

Zoom link:  https://pitp.zoom.us/j/92794475242?pwd=T2Fjbk1lTXRCNnBxVDZabnJqWlAzUT09

 I will talk about new constructions to the parity-violating sector of gravity that can yield large observables, in particular those from inflation. Within this framework, I will demonstrate the potential for seeking gravitational parity-violation in  uncharted regions of parameter space and give hints to novel methods of probing baryogenesis. I will also comment on a few interesting theoretical aspects regarding inflationary  correlators.

Zoom link:  https://pitp.zoom.us/j/95924890817?pwd=MkRyWmV2a3g1dndPNFhoVlQvb3Ixdz09

Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT.  This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity.  Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes.  These edge modes transform under a quantum group, which defines the data associated to an extended topological quantum field theory  Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.  Finally, we give a proposal for obtaining the Ryu Takayanagi formula using the same quantum group edge mode

Zoom link:  https://pitp.zoom.us/j/98275430953?pwd=TzdTUXIvVWU4Ym1jcWRWbkgxZnhMdz09

In any approach to quantum gravity, the quantum representation theory of the "algebra" of Cauchy hypersurface deformations plays a crucial role. Its faithful implementation is a key step towards constructing a valid theory of quantum gravity as it ensures quantum spacetime diffeomorphism covariance. Bergmann and Komar were the first to consider the possibilty of a corresponding quantum "group". Its construction is mathematically challenging in more than 1+1 spacetime dimensions because one leaves the realm of Lie algebras and Lie groups. After an introduction to these concepts, we show that the Bergmann Komar "group" can indeed be faithfully implemented in a weakly self-interacting truncation of 3+1 quantum gravity with two propagating polarisations. We then discuss possible implications for the actual, untruncated theory.

Zoom link:  https://pitp.zoom.us/j/91488383205?pwd=bkxGS0huMGNEYXc3Y2FJSGZHQ0pqQT09

The Lorentzian path sum in causal set theory(CST)  can be defined using the discrete EInstein-Hilbert or Benincasa-Dowker-Glaser(BDG)  action. It has been a long standing question  in CST whether  the path sum is  dominated by a class of non-continuum like layered posets — this would make it much harder to find a dynamically generated continuum approximation —  or whether the BDG action suppresses this contribution.  In this talk I will discuss a series of results that show that to  leading order in the saddle point approximation,  this dominating  class of layered posets is strongly suppressed. Moreover this is true for a  more general class of actions which include the BDG action.   We conclude with some remarks on the interpretation of these results and related  open questions. 

Zoom link:  https://pitp.zoom.us/j/91794153633?pwd=TTFnS0hpQ2s5eFVDM3k5ZDkxcndkUT09

We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with cosmological constant. The construction of spinfoam amplitudes uses the state-integral model of PSL(2,C) Chern-Simons theory and the implementation of simplicity constraint. The formulation has 2 key features: (1) spinfoam amplitudes are all finite, and (2) With suitable boundary data, the semiclassical asymptotics of the vertex amplitude has two oscillatory terms, with phase plus or minus the 4-dimensional Lorentzian Regge action with cosmological constant for the constant curvature 4-simplex.

Zoom link:  https://pitp.zoom.us/j/92219187641?pwd=RUsvcWo2SHFmVTE3NmxDMUZlVEV2UT09

Experimental searches for new fundamental physics are increasingly adopting an Effective Field Theory (EFT) approach, in which the phenomenological effects of the underlying high-energy (UV) physics are parametrised by a series of EFT coefficients that can be readily compared with data.
While pragmatically useful, this begs the question: what UV information can be extracted from our measurements of these EFT coefficients?
In this talk, I will describe how scattering amplitudes techniques ("sum rules") can establish precise connections between EFT coefficients and the underlying UV physics.
In particular, I will focus on recent progress in applying these techniques in cosmology, where they have been used to connect our large-scale measurements of dark energy, gravitational waves and the CMB with properties of the underlying UV completion.

Zoom Link: https://pitp.zoom.us/j/99740767444?pwd=OTMxWlVDYitSTXdKdmlFRWxhdGl1dz09

Do the postulates of quantum mechanics survive in quantum gravity? The probabilistic interpretation of amplitudes, enforced by the unitarity of time evolution, is not guaranteed within the path integral formulation and has to be checked. Leveraging the gravitational path integral, we find a non-perturbative mechanism whereby a sum over smooth geometries leads to isometric rather than unitary evolution, which we demonstrate in simple models of de Sitter quantum gravity. These models include Jackiw-Teitelboim gravity and a minisuperspace approximation to Einstein gravity with a positive cosmological constant. In these models we find that knowledge of bulk physics, even on arbitrarily large timescales, is insufficient to deduce the de Sitter S-matrix.

Zoom Link: https://pitp.zoom.us/j/99363952517?pwd=bm80NzhTRUtwLzQ0YjNBTkFpWVpOdz09

Canonical Quantum Gravity can be considered as a gauge theory of translations. Just like in other gauge theories this implies that physical observables need to be gauge-invariant. Hence, quantities like the metric cannot be observables. This poses new challenges, as this requires to rephrase in the quantum theory how to characterize physics. Moreover, such observables are usually composite. To determine them, the Fröhlich-Morchio-Strocchi mechanism from QFT can be borrowed, to have an augmented perturbative approach.

Zoom Link: https://pitp.zoom.us/j/97927004145?pwd=ekFJaUJSc21UUGdkcDZDWCtpSmdIUT09

We show that if a massive (or charged) body is put in a quantum superposition of spatially separated states in the vicinity of any (Killing) the mere presence of the horizon will eventually destroy the coherence of the superposition. This occurs because, in effect, the long-range fields sourced by the superposition registers on the horizon which forces the radiation of entangling soft gravitons/photons through the horizon. This allows the horizon to harvest “which path” information about the superposition. The electromagnetic decoherence arises only when the superposed particle carries electric charge. However, since all matter sources gravity, the quantum gravitational decoherence applies to all superpositions. We provide estimates of the decoherence time for such quantum superpositions. Additionally, we show that this decoherence is distinct from--and larger than--the decoherence resulting from the presence of thermal radiation from the horizon (i.e. Hawking/Bunch-Davies/Unruh radiation). We believe that the fact that Killing horizons will eventually decohere any quantum superposition may be of fundamental significance for our understanding of the nature of black holes and horizons in quantum gravity. (Based on arXiv:2205.06279 and arXiv: 2301.00026).

Zoom link:  https://pitp.zoom.us/j/95263116767?pwd=amZ6SkROV1lxckVpdzhNbFhYc1ZiQT09

Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. Along this line, a prime question is to find whether gravity is a quantum entity subject to the rules of quantum mechanics. It is fair to say that there are no feasible ideas yet to test the quantum coherent behaviour of gravity directly in a laboratory experiment. I will introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator.  I will show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. I will provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple correlation measurements between two spins: one embedded in each test mass. Fundamentally, the above entanglement is shown to certify the presence of non-zero off-diagonal terms in the coherent state basis of the gravitational field modes.

Zoom link:  https://pitp.zoom.us/j/99584743899?pwd=aHl1cVlpK29ZVDkrdFZyM01GemJJdz09