't Hooft Expansion of 1/2 BPS Wilson Loop

TL;DR

This paper explores the 't Hooft expansion of 1/2 BPS Wilson loops in N=4 SYM, revealing a recursion relation for worldsheet holes and proposing a method to incorporate string coupling effects into the planar result.

Contribution

It introduces a new recursion relation for the worldsheet holes and a technique to include string coupling by transforming the planar result.

Findings

Derived a recursion relation connecting different worldsheet topologies.

Proposed a method to turn on string coupling via integral transformation.

Revisited and extended previous 't Hooft expansion results.

Abstract

We revisit the 't Hooft expansion of 1/2 BPS circular Wilson loop in N=4 SYM studied by Drukker and Gross in hep-th/0010274. We find an interesting recursion relation which relates different number of holes on the worldsheet. We also argue that we can turn on the string coupling by applying a certain integral transformation to the planar result.