The gravitational S-matrix: Erice lectures

TL;DR

These Erice lectures propose the gravitational S-matrix as a sharp, gauge-invariant descriptor of quantum gravity in asymptotically flat spacetimes, highlighting unitarity and observables as central challenges. They develop perturbative gravity, the eikonal regime, and momentum fractionation, connecting high-energy scattering to black-hole formation and the information paradox, and discuss nonlocality as a potential resolution. The notes compare local QFT, string theory, and holographic approaches, arguing that locality must be modified in a controlled, nearly-local way to reconcile unitarity with black-hole physics. The overall message is that a nonperturbative, nearly-local framework—potentially realized via relations to AdS/CFT and relational observables—may be required to resolve the deep tensions between locality, causality, and unitarity in quantum gravity.

Abstract

These lectures discuss an S-matrix approach to quantum gravity, and its relation to more local spacetime approaches. Prominent among the problems of quantum gravity are those of unitarity and observables. In a unitary theory with solutions approximating Minkowski space, the S-matrix (or, in four dimensions, related inclusive probabilities) should be sharply formulated and physical. Features of its perturbative description are reviewed. A successful quantum gravity theory should in particular address the questions posed by the ultrahigh-energy regime. Some control can be gained in this regime by varying the impact parameter as well as the collision energy. However, with decreasing impact parameter gravity becomes strong, first eikonalizing, and then entering the regime where in the classical approximation black holes form. Here one confronts what may be the most profound problem of quantum gravity, that of providing unitary amplitudes, as seen through the information problem of black hole evaporation. Existing approaches to quantum gravity leave a number of unanswered questions in this regime; there are strong indications that new principles and mechanisms are needed, and in particular there is a good case that usual notions of locality are inaccurate. One approach to these questions is investigation of the approximate local dynamics of spacetime, its observables, and its limitations; another is to directly explore properties of the gravitational S-matrix, such as analyticity, crossing, and others implied by gravitational physics.

Figures (15)

• Figure 1: A Feynman diagram representing scattering in the Born approximation.
• Figure 2: Addition of a soft graviton to a diagram.
• Figure 3: A proposed "phase diagram" of different regimes for gravitational scattering. In particular, we consider the effect of decreasing impact parameter, at fixed ultraplanckian energy, as indicated by the arrow. NR indicates the regime where higher-dimension operators are expected to be important.
• Figure 4: A ladder diagram, with multiple graviton exchange. (Note that the crossed lines do not connect.)
• Figure 5: The one-loop ladder diagram is obtained by combining two tree diagrams.