Perturbative Quantum Gravity and its Relation to Gauge Theory

TL;DR

This review explores the deep connections between gauge theory and gravity scattering amplitudes, highlighting how gauge theory techniques can systematically construct quantum gravity corrections and reveal improved ultraviolet behavior.

Contribution

It details the relationship between gauge theory and gravity amplitudes, and introduces a unitarity-based method for perturbative quantum gravity calculations.

Findings

Gravity amplitudes can be expressed as products of gauge theory amplitudes.

Unitarity methods enable systematic loop correction calculations in quantum gravity.

Maximally supersymmetric gravity is less divergent in the ultraviolet than previously believed.

Abstract

In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on D-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input the gravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.