Quantum Gravity

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.  The results can be compared to expectations based on potential counterterms that can be constructed using (conjectured) superspace formalisms or nonlinear symmetry constraints.  Interestingly, the critical ultraviolet dimension in which N=8 supergravity first diverges is equal to that for N=4 super-Yang-Mills theory through four loops.  If this statement were to hold to all loop orders, then N=8 supergravity would represent a perturbatively finite, point-like theory of quantum gravity in four dimensions.  In this talk, I will review all of this recent progress.

Causal dynamical triangulations (CDT) define a nonperturbative path integral for quantum gravity as a sum over triangulations. Causality is enforced on the kinematical level by means of a preferred
foliation.

In this talk I present a new model of dynamical triangulations based on Lorentzian building blocks, where the triangulations in general do not have such a preferred foliation. The essential ingredients of the new model are a local causality constraint and a consistency condition on the global flow of time. After a compact review on CDT I discuss the theoretical aspects of the new model in 1+1 and 2+1 dimensions, followed by a presentation of numerical results in 2+1 dimensions. These results show that the new model and CDT have similar long-distance properties in 2+1 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
gravity), news on the controversy between doing things the Lorentzian or the Euclidean way, and new results on the role of the preferred time slicing in CDT - all hopefully worth your while!

Causal set quantum gravity is based on the marriage between the concept of causality as an organising principle more basic even than space or time and fundamental atomicity. Causal sets suggest novel possibilities for "dynamical laws" in which spacetime grows by the accumulation of new spacetime atoms, potentially realising within physics C.D. Broad's concept of a growing block universe
in which the past is real and the future is not. To do justice to relativity and general covariance, the atoms must accumulate in a partial order, exactly the order that the atoms have physically amongst themselves. That this is possible is demonstrated by the Rideout-Sorkin Classical Stochastic Growth models. This proof of concept -- of the compatibility of relativity and ``becoming'' -- is, however, classical and is challenged by the global character of the physical world within a path integral framework for quantum theory. Out of the struggle to reconcile the global and local natures of the physical world may arise a quantal dynamics for causal sets.