I will present a brief review of large-N tensor models and their applications in quantum gravity. On the one hand, they provide a general platform to investigate random geometry in an arbitrary number of dimensions, in analogy with the matrix models approach to two-dimensional quantum gravity. Previously known universality classes of random geometries have been identified in this context, with continuous random trees acting as strong attractors. On the other hand, the same combinatorial structure supports a generic family of large-N quantum theories, collectively known as melonic theories. Being largely solvable, they have opened a new window into strongly-coupled quantum theory, and via holography, into quantum gravity. Prime examples are provided by the SYK model and generalizations, which capture essential features of Jackiw-Teitelboim gravity.
Recent discoveries suggest that semiclassical gravity is more consistent with unitarity than previously believed. I will argue that it makes predictions for the measurements of asymptotic observers that are in complete accord with the idea that black holes are ordinary quantum systems, with states counted by the Bekenstein-Hawking formula. The argument uses the semiclassical gravitational path integral, incorporating newly discovered `spacetime wormhole' topologies. These new ideas revive an old paradigm, relating the information problem to the physics of baby universes.
I will review advances for gravity in asymptotically flat spacetimes arising from investigations into their structure in the infrared. The recently-discovered infinite-dimensional symmetries of the scattering problem is the central result underlying much of the progress. Key examples include symmetry-based explanations for the previously-observed universal nature of infrared phenomena including soft theorems and memory effects. Moreover, the appearance of a Virasoro symmetry among the symmetries of four-dimensional gravity has led to a proposal for holography in which the scattering amplitudes in quantum gravity are dual to correlation functions of a two-dimensional conformal theory. The other infinite-dimensional symmetry groups place additional non-trivial constraints on the dual theory.
I will highlight cosmological consequences of models inspired from string theory or non-perturbative approaches to QG. In particular, I will address the initial singularity, inflation and the late-time accelerated expansion. I will then briefly discuss how recent gravitational waves data can provide a test for some QG models.
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.