Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM

TL;DR

This paper proposes a closed-form expression for correlators of BPS Wilson loops on a two-sphere in N=4 SYM, valid at all couplings and ranks, supported by perturbative checks and string theory comparisons.

Contribution

It introduces a novel, all-coupling formula for Wilson loop correlators in N=4 SYM, linking them to two-dimensional gauge theories and providing evidence for protected operators.

Findings

Perturbative checks at order g^4 and g^6 support the formula.

Logarithmic corrections vanish in the shrinking loop limit.

Preliminary agreement with string dual calculations at strong coupling.

Abstract

We study the correlators of a recently discovered family of BPS Wilson loops in ${\cal N}=4$ supersymmetric U(N) Yang-Mills theory. When the contours lie on a two-sphere in the space-time, we propose a closed expression that is valid for all values of the coupling constant $g$ and for any rank $N$, by exploiting the suspected relation with two-dimensional gauge theories. We check this formula perturbatively at order ${\cal O}(g^4)$ for two latitude Wilson loops and we show that, in the limit where one of the loops shrinks to a point, logarithmic corrections in the shrinking radius are absent at ${\cal O}(g^6)$. This last result strongly supports the validity of our general expression and suggests the existence of a peculiar protected local operator arising in the OPE of the Wilson loop. At strong coupling we compare our result to the string dual of the ${\cal N}=4$ SYM correlator in the limit of large separation, presenting some preliminary evidence for the agreement.