More exact predictions of SUSYM for string theory

TL;DR

This paper studies the circular Wilson loop in ${\cal N}=4$ SYM and computes the OPE coefficients with an infinite family of chiral primary operators by resumming planar rainbow Feynman diagrams. The authors demonstrate that leading radiative corrections from diagrams with internal vertices cancel, and they conjecture cancellations persist to all orders in perturbation theory, yielding exact results in the large-$N$ limit. The resulting OPE coefficients are nontrivial functions of the 't Hooft coupling $\lambda$ that interpolate between weak and strong coupling, with strong-coupling limits matching AdS/CFT predictions and reproducing the expected universal $\sqrt{\lambda}$ scaling. These findings provide a precise, checkable bridge between perturbative gauge theory and string-theoretic descriptions, and they offer predictions for subleading stringy corrections in the dual AdS$_5\times$S^5 background.

Abstract

We compute the coefficients of an infinite family of chiral primary operators in the local operator expansion of a circular Wilson loop in N=4 supersymmetric Yang-Mills theory. The computation sums all planar rainbow Feynman graphs. We argue that radiative corrections from planar graphs with internal vertices cancel in leading orders and we conjecture that they cancel to all orders in perturbation theory. The coefficients are non-trivial functions of the 'tHooft coupling and their strong coupling limits are in exact agreement with those previously computed using the AdS/CFT correspondence. They predict the subleading orders in strong coupling and could in principle be compared with string theory calculations.

Figures (3)

• Figure 1: A typical diagram that contributes to the correlator of the circular Wilson loop with the dimension $k$ CPO.
• Figure 2: Leading radiative corrections to the correlator of the Wilson loop operator with the $k=2$ CPO. These are not taken into account by the sum over planar rainbow graphs which were computed in Sec.3.
• Figure 3: The contribution to the leading term in $R^2/L^4$ of the diagrams in fig.\ref{['diagr2']}b-e are given by these 2-loop diagrams. This combination of diagrams is known to vanish due to the non-renormalization theorem of the 2-point function of the CPO.