Higher loop mixed correlators in N=4 SYM

TL;DR

This paper calculates the two-loop correction to a specific correlator in N=4 SYM, confirming known three-loop cusp anomalous dimension results and introducing a twistor-based integrand representation.

Contribution

It provides an analytical two-loop computation of a mixed correlator in N=4 SYM and introduces a twistor variable representation of the loop integrand.

Findings

Reproduces the three-loop cusp anomalous dimension from two-loop correlator integration.

Develops a dual scattering amplitude approach for the calculation.

Presents a simple twistor variable representation of the loop integrand.

Abstract

We compute analytically the two-loop contribution to the correlation function of the Lagrangian with a four-sided light-like (or null) Wilson loop in N=4 super Yang-Mills. As a non-trivial test of our result, we reproduce the three-loop value of the cusp anomalous dimension upon integration over the insertion point of the Lagrangian. The method we used involved calculating a dual scattering amplitude. Moreover, we give a simple representation of the loop integrand of the latter in twistor variables.