Quantum Gravity

I will describe the relevant representation theory that allows to think of all components of fermions of a single generation of the Standard Model as components of a single Weyl spinor of an orthogonal group whose complexification is SO(14,C). There are then only two real forms that do not lead to fermion doubling. One of these real forms is the split signature orthogonal group SO(7,7). I will describe some exceptional phenomena that occur for the orthogonal groups in 14 dimensions, and then specifically for this real form. The real form SO(7,7) suggests a link to generalised geometry, which I will describe. I will also describe why spinors in general are really differential forms in disguise. 

Tensor models are generalizations of vector and matrix models. They have been introduced in quantum gravity and are also relevant in the SYK model. I will mostly focus on models with a U(N)^d-invariance where d is the number of indices of the complex tensor, and a special case at d=3 with O(N)^3 invariance. The interactions and observables are then labeled by (d-1)-dimensional triangulations of PL pseudo-manifolds. The main result of this talk is the large N limit of observables corresponding to 2-dimensional planar triangulations at d=3. In particular, models using such observables as interactions have a large N limit exactly solvable as it is Gaussian. If time permits, I will also discuss interesting questions in the field: models which are non-Gaussian at large N, the enumeration of triangulations of PL-manifolds, matrix model representation of some tensor models, etc.

The goal of this series is to collect various different formulations of General Relativity, with emphasis on four spacetime dimensions and formulations that use differential forms. The (non-exhaustive) list of formulations to be covered is per this plan:

Lecture 1): Motivations, followed by the usual Einstein-Hilbert to start with, first order Palatini, second order pure affine connection Eddington-Schroedinger.

Lecture 2) Cartan's geometry of soldering. First order Einstein-Cartan tetrad formulation, second order pure spin connection formulation, MacDowell-Mansouri formulation.

Lecture 3) Non-chiral BF-type formulations. Explicit pure spin connection Lagrangian, field redefinitions, BF plus potential for the 2-form field formulation.

Lecture 4) Chiral formulations in four dimensions. Chiral Einstein-Cartan, Plebanski formulation, pure SU(2) connection formulation, SU(2) BF plus potential for the 2-form field. Self-dual gravity. Concluding remarks. 

The goal of this series is to collect various different formulations of General Relativity, with emphasis on four spacetime dimensions and formulations that use differential forms. The (non-exhaustive) list of formulations to be covered is per this plan:

Lecture 1): Motivations, followed by the usual Einstein-Hilbert to start with, first order Palatini, second order pure affine connection Eddington-Schroedinger.

Lecture 2) Cartan's geometry of soldering. First order Einstein-Cartan tetrad formulation, second order pure spin connection formulation, MacDowell-Mansouri formulation.

Lecture 3) Non-chiral BF-type formulations. Explicit pure spin connection Lagrangian, field redefinitions, BF plus potential for the 2-form field formulation.

Lecture 4) Chiral formulations in four dimensions. Chiral Einstein-Cartan, Plebanski formulation, pure SU(2) connection formulation, SU(2) BF plus potential for the 2-form field. Self-dual gravity. Concluding remarks. 

The goal of this series is to collect various different formulations of General Relativity, with emphasis on four spacetime dimensions and formulations that use differential forms. The (non-exhaustive) list of formulations to be covered is per this plan:

Lecture 1): Motivations, followed by the usual Einstein-Hilbert to start with, first order Palatini, second order pure affine connection Eddington-Schroedinger.

Lecture 2) Cartan's geometry of soldering. First order Einstein-Cartan tetrad formulation, second order pure spin connection formulation, MacDowell-Mansouri formulation.

Lecture 3) Non-chiral BF-type formulations. Explicit pure spin connection Lagrangian, field redefinitions, BF plus potential for the 2-form field formulation.

Lecture 4) Chiral formulations in four dimensions. Chiral Einstein-Cartan, Plebanski formulation, pure SU(2) connection formulation, SU(2) BF plus potential for the 2-form field. Self-dual gravity. Concluding remarks. 

The goal of this series is to collect various different formulations of General Relativity, with emphasis on four spacetime dimensions and formulations that use differential forms. The (non-exhaustive) list of formulations to be covered is per this plan:

Lecture 1): Motivations, followed by the usual Einstein-Hilbert to start with, first order Palatini, second order pure affine connection Eddington-Schroedinger.

Lecture 2) Cartan's geometry of soldering. First order Einstein-Cartan tetrad formulation, second order pure spin connection formulation, MacDowell-Mansouri formulation.

Lecture 3) Non-chiral BF-type formulations. Explicit pure spin connection Lagrangian, field redefinitions, BF plus potential for the 2-form field formulation.

Lecture 4) Chiral formulations in four dimensions. Chiral Einstein-Cartan, Plebanski formulation, pure SU(2) connection formulation, SU(2) BF plus potential for the 2-form field. Self-dual gravity. Concluding remarks. 

Black hole entropy is a robust prediction of quantum gravity with no observational test to date. We use the Bekenstein-Hawking entropy formula to determine the probability distribution of the spin of black holes at equilibrium in the microcanonical ensemble. We argue that this ensemble is relevant for black holes formed in the early universe and predicts the existence of a population of black holes with zero spin. Observations of such a population at LIGO, Virgo, and future gravitational wave observatories would provide the first experimental test of the statistical nature of black hole entropy.

I argue that we do not understand gauge theory as well as we think when boundaries are present. I will briefly explain the conceptual and technical issues that arise at the boundary.  I will then propose a tentative resolution, which requires us to think of theories not in spacetime, but in field-space. 

Black holes are like bells; once perturbed they will relax through the emission of characteristic waves. The frequency spectrum of these waves is independent of the initial perturbation and, hence, can be thought of as a `fingerprint' of the black hole. Since the 1970s scientists have considered the possibility of using these characteristic modes of oscillation to identify astrophysical black holes. With the recent detection of gravitational waves, this idea has started to turn into reality.
Inspired by the black hole-fluid analogy, we demonstrate the universality of the black-hole relaxation process through the observation of characteristic modes emitted by a hydrodynamical vortex flow. The characteristic frequency spectrum is measured and agrees with theoretical predictions obtained using techniques developed for astrophysical black holes. Our findings allow for the first identification of a hydrodynamical vortex flow through its characteristic waves.
The flow velocities inferred from the observed spectrum agree with a direct flow measurement. Our approach establishes a non-invasive method, applicable to vortex flows in fluids and superfluids alike, to identify the wave-current interactions and hence the effective field theories describing such systems.

We present a consistent theory of classical gravity coupled to quantum field theory. The dynamics is linear in the density matrix, completely positive and trace-preserving, and reduces to Einstein's equations in the classical limit. Several no-go theorems are evaded since the assumption that gravity is classical necessarily modifies the dynamical laws of quantum mechanics -- the theory must be fundamentally stochastic involving finite sized and probabilistic jumps in space-time and in the quantum field. Nonetheless the quantum state of the system can remain pure conditioned on the classical degrees of freedom. The measurement postulate of quantum mechanics is not needed since the interaction of the quantum degrees of freedom with classical space-time necessarily causes collapse of the wave-function. More generally, we derive a form of classical-quantum dynamics using a non-commuting divergence which has as its limit deterministic classical Hamiltonian evolution, and which doesn't suffer from the pathologies of the semi-classical theory. Details at http://arxiv.org/abs/1811.03116

The path integral approach to quantum gravity has given us many interesting results in the semiclassical regime. However, the canonical path integral for General Relativity still poses a variety of conceptual and computational challenges. To probe the deep quantum regime, Path Integral Monte Carlo (PIMC) techniques are being used successfully in approaches like Causal Dynamical Triangulations and Causal Set Theory. 

In this talk I will discuss how we can apply PIMC techniques to make the canonical Path Integral amenable to computation using matter-time. I will present results from PIMC simulations of homogeneous & isotropic cosmologies, and discuss the extension of this technique to anisotropic as well as inhomogeneous settings. 

I show that Unruh effect can be associated with the partitioning of the real line, and derived from the basic representation theory of the group of affine transformations in one dimension. This result shows that thermal distributions naturally emerge in connecting quantum
states belonging to representations related to distinct notions of translational symmetry.