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

TL;DR

This paper computes the two-loop expectation value of two circular Wilson loops in N=4 supersymmetric Yang-Mills theory, revealing finiteness and subleading corrections, and provides insights into the strong-coupling regime via AdS/CFT.

Contribution

It presents the first complete two-loop calculation of Wilson loops in N=4 SYM, showing finiteness and new corrections beyond previous lower-order results.

Findings

The two-loop result is finite without renormalization.

Internal vertex diagrams contribute non-trivially at two loops.

Evidence suggests strong-coupling results may sum all planar diagrams.

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.