The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory

TL;DR

This paper investigates the cross anomalous dimension matrix in N=4 supersymmetric Yang--Mills theory, analyzing its behavior at both weak and strong coupling, and highlighting its potential in integrability studies.

Contribution

It provides a detailed analysis of the cross anomalous dimension in N=4 SYM at weak and strong coupling, connecting it to the cusp anomalous dimension and phase transitions.

Findings

Coefficients expressed via cusp anomalous dimension

Gross--Ooguri phase transition observed at strong coupling

Cross anomalous dimension linked to integrability approaches

Abstract

The cross or soft anomalous dimension matrix describes the renormalization of Wilson loops with a self-intersection and is an important object in the study of infrared divergences of scattering amplitudes. In this paper it is studied for the Maldacena--Wilson loop in N=4 supersymmetric Yang--Mills theory and Euclidean kinematics. We consider both the strong-coupling description in terms of minimal surfaces in AdS5 as well as the weak-coupling side up to the two-loop level. In either case, the coefficients of the cross anomalous dimension matrix can be expressed in terms of the cusp anomalous dimension. The strong-coupling description displays a Gross--Ooguri phase transition and we argue that the cross anomalous dimension is an interesting object to study in an integrability-based approach.