This series consists of talks in the area of Quantum Gravity.
I will present a generalization of the spinor approach of Euclidean loop quantum gravity to the 3D Lorentzian case, where the gauge group is the noncompact SU(1,1). The key tool of this generalization is the recoupling theory between unitary infinite-dimensional representations and non-unitary finite-dimensional ones, needed to generalize the Wigner-Eckart theorem to tensor operators for SU(1,1).
In quantum gravity, observables must be diffeomorphism-invariant. Such observables are nonlocal, in contrast with the standard assumption of locality in flat spacetime quantum field theory. I will show how to construct 'gravitationally dressed' observables in linearized gravity that become local in the weak gravity limit, and whose corrections to exact locality are characterized by the Newtonian potential. One can attempt to make these observables more local by concentrating gravitational field lines into a smaller solid angle.
In this talk, I will review the Refined Gribov-Zwanziger framework designed to deal with the so-called Gribov copies in Yang-Mills theories and its standard BRST soft breaking. I will show that, within this scenario, the BRST transformations are modified in the non-perturbative regime in order to be a symmetry of the model. This fact has been supported by recent lattice simulations and opens a new avenue for the investigation of non-perturbative effects in Yang-Mills theories.
The Hartle-Hawking (HH) no-boundary proposal provides a Euclidean path integral prescription for a measure on the space of all possible initial conditions. Apart from saddle point and minisuper-space calculations, it is hard to obtain results using the unregulated path integral. A promising choice of spacetime regularisation comes from the causal set (CST) approach to quantum gravity. Using analytic results as well as Markov Chain Monte Carlo and numerical integration methods we obtain the HH wave function in a theory of non-perturbative 2d CST.
The kinematical framework of canonical loop quantum gravity has mostly been studied in the context of compact Cauchy slices. However many key physical notions such as total energy and momentum require the use of asymptotically flat boundary conditions (and hence non-compact slices). We present a quantum kinematics, based on the Koslowski-Sahlmann representation, that successfully incorporates such asymptotically flat boundary conditions. Based on joint work with Madhavan Varadarajan.
I will describe a proposal for a generalization of the BMS group in which the conformal isometries of the sphere (Lorentz group) are replaced by arbitrary sphere diffeomorphisms. I describe the computation of canonical charges and show that the associated Ward identities are equivalent to the Cachazo-Strominger subleading soft graviton formula. Based on joint work with Alok Laddha.
We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions.
We will briefly review the issue of "information loss" during the Hawking evaporation of a black hole, and argue that the quantum dynamical reduction theories, which have been developed to address the measurement problem in quantum mechanics, possess the elements to diffuse the ``paradox” at the qualitative and at the quantitative level, leading to what seems to be an overall coherent picture.
Although the inflationary predictions for the primordial power spectrum of density inhomogeneities seem very successful, there is an obscure part in our understanding of the emergence of the seeds of cosmic structure: How does a universe which at one pint in time is described by a state that is fully homogeneous and isotropic, evolve into a state that is not, given that the dynamics does not contain any source for the undoing of such symmetry?