The gravitational cusp anomalous dimension from AdS space

TL;DR

This paper extends a geometric approach to compute cusp anomalous dimensions from gauge theories to quantum gravity, revealing a unified framework that interpolates between QED and gravity.

Contribution

It demonstrates how the cusp anomalous dimension in quantum gravity can be derived using the Newtonian limit, unifying gauge and gravity theories within a common formulation.

Findings

Cusp anomalous dimension in gravity is one loop exact.

A continuous parameter interpolates between QED and gravity cases.

The geometric picture applies to both gauge and gravity Wilson lines.

Abstract

Recently a new picture has been developed for examining Wilson lines, and the corresponding anomalous dimensions which govern their renormalization properties. By making a particular coordinate transform, the calculation of the cusp anomalous dimension in QED or QCD can be related to the energy of a pair of static charges in Euclidean Anti-de-Sitter (AdS) space. This paper shows how the same picture can be used to describe Wilson lines in quantum gravity. We show how the relevant cusp anomalous dimension (which has recently been shown to be one loop exact) can be obtained using the Newtonian limit of General Relativity. We also show how both the QED and gravity cases emerge as special cases of a general formulation, and that a continuous parameter exists which interpolates between them. The results may be useful in examining the relations between gauge and gravity theories.