Operator product expansion of higher rank Wilson loops from D-branes and matrix models

TL;DR

This work computes the operator product expansion coefficients for circular Wilson loops in higher representations of N=4 SYM by harnessing the holographic description in terms of D3$_k$ and D5$_k$ branes with electric flux in AdS$_5\times S^5$. The authors derive explicit OPE coefficients for couplings to chiral primaries both from brane fluctuations (D3 and D5) and from the normal matrix model, obtaining exact agreement in symmetric and antisymmetric cases. They also express the results in closed forms involving special functions (e.g., Chebyshev and Gegenbauer polynomials) and verify the string limit as $k/N\to0$. The findings reinforce the holographic dictionary for higher-rank Wilson loops and provide a nonperturbative cross-check via matrix models, suggesting extensions to other KK modes and operator classes.

Abstract

In this paper we study correlation functions of circular Wilson loops in higher dimensional representations with chiral primary operators of N=4 super Yang-Mills theory. This is done using the recently established relation between higher rank Wilson loops in gauge theory and D-branes with electric fluxes in supergravity. We verify our results with a matrix model computation, finding perfect agreement in both the symmetric and the antisymmetric case.