Gravitational cusp anomalous dimension from AdS space

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 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.

Figure 1

The emission of a graviton from an external scalar line.

Figure 2

(a) Wilson loop contour in Minkowski space used for the calculation of the Newtonian potential; (b) the relevant one-loop diagram.

Figure 3

The 3-surface used to normalize the coefficient $A_1$ in the general solution to the homogeneous Newton equation. The horizontal plane is representative of the spacelike directions, where the radial distance in this plane represents $\beta$.

Figure 4

Diagram entering the calculation of the cusp anomalous dimension.