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

Zoom link: https://pitp.zoom.us/j/96212372067?pwd=dWVaUFFFc3c5NTlVTDFHOGhCV2pXdz09