Two Loops to Two Loops in N=4 Supersymmetric Yang-Mills Theory

TL;DR

This work analyzes two Maldacena-Wilson loops in ${\\cal N}=4$ SYM, focusing on a two-loop perturbative calculation in the planar limit with $\\\lambda= N g^2$ finite. The authors perform a complete ${\\cal O}(g^6)$ study for two parallel axisymmetric circles, showing that subtle bulk-boundary cancellations render the observable finite at this order, while internal vertex (nonladder) diagrams no longer cancel in general. In the static-potential limit (infinite anti-parallel lines) they analytically and numerically extract the ladder and nonladder contributions, finding that nonladder diagrams are nonzero but subleading, with IY-type graphs producing the largest subleading terms and partially canceling certain ladder subleading pieces. These results provide perturbative evidence that AdS/CFT predictions may capture the full planar dynamics in the appropriate limits, while highlighting subtleties in finiteness and the role of nonladder diagrams for precise weak-to-strong coupling matching.

Abstract

We present a full two-loop O(g^6) perturbative field theoretic calculation of the expectation value of two circular Maldacena-Wilson loops in D=4 N=4 supersymmetric U(N) gauge theory. It is demonstrated that, after taking into account very subtle cancellations of bulk and boundary divergences, the result is completely finite without any renormalization. As opposed to previous lower order calculations existing in the literature, internal vertex diagrams no longer cancel identically and lead to subleading corrections to the dominant ladder diagrams. Taking limits, we proceed to extract the two-loop static potential corresponding to two infinite anti-parallel lines. Our result gives some evidence that the existing strong-coupling calculations using the AdS/CFT conjecture might sum up the full set of large N planar Feynman diagrams.