This series consists of talks in the area of Quantum Gravity.
The functional renormalization group
is a tool in the systematic search for Euclidean QFTs that works with
very little input: All one needs to specify is a field content,
symmetries and a notion of locality. The functional renormalization
group then allows one to scan this theory space for bare actions for
which the path integral can be performed nonperturbatively. These
actions appear as fixed points (and relevant deformations) of the
renormalization group flow (so-called asymptotic safety). Such a
late physicist John Wheeler, was renowned for his Socratic method of conducting
physics discussions. "Why is general relativity the way it is? What makes
it special?" were reportedly questions one should expect in his
presence. There are different answers to these questions, each requiring a set
of assumptions - which Wheeler would likely question again - and each bringing
with it new insights into physics as a whole. This talk will put forward
new principles for deriving general relativity. Perhaps more than is the case
AdS/CFT is a duality
relating the degrees of freedom in a D dimensional bulk gravity theory to a (D-1) dimensional theory living on the boundary. I will argue that in fact the boundary theory contains only a subset of the bulk observables. For each state of the boundary theory, there are multiple bulk states dual to it, which can be operationally distinguished by observers who fall across event horizons. Based on arXiv:1210.3590.
We argue that the
scale-free spectrum that is observed in the cosmic microwave background is the
result of a phase transition in the early universe. The observed tilt of
the spectrum, which has been measured to be 0.04, is shown to be equal to the
anomalous scaling dimension of the correlation function. The phase
transition replaces inflation as the mechanism that produces this spectrum. The tilt further indicates that there is a fundamental small length scale in
nature that we have not yet observed in any other way.
A defining feature of holographic dualities is that, along with the bulk equations of motion, boundary correlators at any given time t determine those of observables deep in the bulk. We argue that this property emerges from the bulk gravitational Gauss law together with bulk quantum entanglement as embodied in the Reeh-Schlieder theorem. Stringy bulk degrees of freedom are not required and play little role even when they exist. As an example we study a toy model whose matter sector is a free scalar field.
Recently powerful techniques have emerged for performing multi-loop computations of scattering amplitudes in quantum gravity and supergravity. These techniques include generalized unitarity and the double-copy property, related to color-kinematics duality in gauge theory. Using these techniques, the ultraviolet divergence structure of N=8 supergravity, and more recently pure N=4 supergravity, have been assessed, not only in four space-time dimensions but also in higher dimensions.
By way of presenting some classic and many new results, my talk will indulge shamelessly in
advertising "Causal Dynamical Triangulations (CDT)" as a hands-on approach to nonperturbative quantum gravity that reaches where other approaches currently don't. After summarizing the rationale and basic ingredients of CDT quantum gravity and some of its key findings (like the emergence of a classical de Sitter space), I will focus on some very recent results: how we uncovered the presence of a second-order phase transition (so far unique in 4D quantum
theory techniques allow reliable quantum calculations in general relativity at
low energy. After a review of these techniques, I will discuss the attempts to
define the gravitational corrections to running gauge couplings and to the
couplings of gravity itself. I will also describe an attempt to understand the
relation between the effective field theory and Asymptotic Safety in the region
where they overlap.