This series consists of talks in the area of Quantum Gravity.
We present results from a study of Euclidean dynamical triangulations in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior, and that once this tuning is performed, our simulations provide evidence in support of the asymptotic safety scenario for gravity. We discuss our motivation for the tuning and present our numerical results. Finally, we discuss what our simulations imply for the dimension of the ultraviolet critical surface, which sets the number of free parameters in the theory.
In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.
The fact that the Einstein-Hilbert action, by itself, does not lead to a well-posed variational principle has become textbook knowledge. It can be made well-posed by the addition of suitable boundary terms. There are many boundary terms available in the literature, of which the most famous and most widely used is the Gibbons-Hawking-York (GHY) boundary term. The GHY term is ostensibly defined only for a non-null boundary. There have been very few efforts in the literature to extend its definition to null boundaries.
I will present recent result on constructing effective quantum gravity theory as a locally covariant QFT. The approach I advocate uses the BV formalism for dealing with the gauge freedom and Epstein-Glaser renormalization to control the UV divergences. I will show how gauge invariant observables that satisfy a weak notion of locality can be constructed in this framework and I will sketch the argument for perturbative background independence. Recently these ideas were applied to models relevant in cosmology.
In this talk I discuss the effects of nonlinear backreaction of small scale density inhomogeneities in general relativistic cosmology. It has been proposed that in an inhomogeneous universe, nonlinear terms in the Einstein equation could, if properly averaged and taken into account, affect the large scale Friedmannian evolution of the universe. In particular, it was hoped that these terms might mimic a cosmological constant and eliminate the need for dark energy. After reviewing some of these approaches, and some of their flaws, I will describe a perturbative framework (developed with R.
The precise determination of the entanglement of an interacting quantum many-body systems is now appreciated as an indispensable tool to identify the fundamental character of the ground state of such systems. This is particularly true for unconventional ground states harbouring non-local topological order or so-called quantum spin liquids that evade a standard description in terms of correlation functions.
The collection of all Dirac operators for a given fermion space defines its space of geometries.
Formally integrating over this space of geometries can be used to define a path integral and a thus a theory of quantum gravity.
In general this expression is complicated, however for fuzzy spaces a simple expression for the general form of the Dirac operator exists. This simple expression allows us to explore the space of geometries using Markov Chain Monte Carlo methods and thus examine the path integral in a manner similar to that used in CDT.