Quantum Gravity 2020
A quantum theory of gravity is expected to be described by a Hilbert space endowed with additional mathematical structure appropriate for describing gravitational physics. I discuss aspects of this structure that can be inferred perturbatively, along with connections to arguments for holography and nonperturbative questions.
The study of scattering amplitudes has uncovered extraordinary dualities linking real-world particles such as gravitons, gluons, and pions. We discuss how these developments have been amalgamated with classic tools from effective field theory to derive new results relevant to the search for gravitational waves at LIGO. This approach has produced now state-of-the-art results on conservative orbital dynamics of binary black holes in the post-Minkowskian expansion. We also comment on recent work extending this framework to include tidal effects and spin.
Analogue gravity summarises an effort to mimic physical processes that occur in the interplay between general relativity and field theory in a controlled laboratory environment. The aim is to provide insights in phenomena that would otherwise elude observation: when gravitational interactions are strong, when quantum effects are important, and/or on length scales that stretch far beyond the observable Universe. The most promising analogue gravity systems up-to-date are fluids, superfluids, superconducting circuits, ultra-cold atoms and optical systems.
I will begin with a short review of causal set theory (CST) focusing on the features that distinguish it from other approaches to quantum gravity. Most striking is a characteristic non-locality due to the Lorentz non-violating Poisson-discreteness in the continuum approximation. The discrete causal structure is rich enough, however, to extract local continuum geometric information, with geometric and topological observables corresponding to order-invariants in the causal set.
It has taken several decades of exploring statistical models of quantum gravity (aka nonperturbative gravitational path integrals) to understand how diffeomorphism-invariance, unitarity and the presence of a causal structure can be simultaneously accounted for in a lattice gravity framework. Causal Dynamical Triangulations (CDT) incorporates all of these features and provides a toolbox for extracting quantitative results from a first-principles quantum formulation, with very few free parameters.
This talk will feature a brief introduction to the gravitational asymptotic safety program before reviewing the current status of the field. Motivated by recent developments, I will introduce the form factor formulation of the quantum effective action and explain how various quantum gravity programs can be embedded into this framework. Finally, I will discuss a novel gravity-matter model whose scattering amplitudes exhibit all features expected from Asymptotic Safety.
I will review some developments in horizon thermodynamics from the past few years, highlighting especially the distinct notions of entropy that seem to apply to dynamically evolving black holes, and their extension from classical to semiclassical gravity.
Gravity is unique among the other forces in that within general relativity we are able to do calculations which, when properly interpreted, give us information about non-perturbative quantum gravity. A classic example is Bekenstein and Hawking's calculation of the entropy of a black hole, and a more recent example is the calculation of the ``Page curve'' for certain evaporating black holes. A common feature of both of these calculations is that they compute entropies without using von Neumann's formula S=-Tr(\rho \log \rho).
I will summarise the main achievements of loop quantum gravity and provide my view on the issues that I consider of central importance for present and future efforts.