Quantum Gravity

Effective field theory is a computationally powerful and flexible theoretical framework, finding application in many areas of physics. In particle physics, Weinberg’s folk theorem also promises that any theory that reproduces the predictions of the Standard Model will, at low energies, look like an effective field theory. In one sense the power of this framework should be a cause for pride in the progress of physics and discovery of real structural features of the world. But given the inability to fully unite quantum theory and gravity into a consistent theoretical picture, there is also cause for pessimism: indirect tests of candidate theories of quantum gravity will ultimately reduce to something like an effective field theory, undermining efforts to find low-energy windows into new physics. One way around this pessimism is to look at where and why effective field theory breaks down in current physical theories. I will point to familiar breakdowns (the cosmological constant, inflation, the hierarchy problem), offering a take on what these breakdowns tell us about the shape of physics beyond the Standard Model. Cracks in the wall of effective field theory allow for a dim glimpse of what might lie beyond.

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