One-loop Structure of Higher Rank Wilson Loops in AdS/CFT

TL;DR

This paper investigates the next-to-leading order corrections to higher rank Wilson loops in AdS/CFT, comparing matrix model predictions with string theory results, revealing agreement in functional form but discrepancies in coefficients.

Contribution

It provides the first detailed analysis of the one-loop structure of higher rank Wilson loops in AdS/CFT, highlighting the match and mismatch with string theory calculations.

Findings

Functional dependence on representation rank matches between matrix model and string theory.

Numerical coefficients differ, indicating potential subtleties in the correspondence.

Advances understanding of quantum corrections in holographic Wilson loops.

Abstract

The half-supersymmetric Wilson loop in $\mathcal N=4$ SYM is arguably the central non-local operator in the AdS/CFT correspondence. On the field theory side, the vacuum expectation values of Wilson loops in arbitrary representations of $SU(N)$ are captured to all orders in perturbation theory by a Gaussian matrix model. Of prominent interest are the $k$-symmetric and $k$-antisymmetric representations, whose gravitational description is given in terms of D3- and D5-branes, respectively, with fluxes in their world volumes. At leading order in $N$ and $\lambda$ the agreement in both cases is exact. In this note we explore the structure of the next-to-leading order correction in the matrix model and compare with existing string theory calculations. We find agreement in the functional dependence on $k$ but a mismatch in the numerical coefficients.