All-genus calculation of Wilson loops using D-branes

TL;DR

This paper develops a D-brane approach to compute Wilson loops in AdS/CFT, providing solutions that match string results at weak coupling and include higher genus corrections, aligning with matrix model predictions.

Contribution

It introduces D-brane solutions for Wilson loops that improve upon string world-sheet methods, capturing higher genus effects and matching matrix model results.

Findings

D-brane solutions for Wilson loops are found.

Results agree with string calculations at small coupling.

Higher genus corrections are captured at leading order.

Abstract

The standard prescription for calculating a Wilson loop in the AdS/CFT correspondence is by a string world-sheet ending along the loop at the boundary of AdS. For a multiply wrapped Wilson loop this leads to many coincident strings, which may interact among themselves. In such cases a better description of the system is in terms of a D3-brane carrying electric flux. We find such solutions for the single straight line and the circular loop. The action agrees with the string calculation at small coupling and in addition captures all the higher genus corrections at leading order in alpha'. The resulting expression is in remarkable agreement with that found from a zero dimensional Gaussian matrix model.