Precision matching of circular Wilson loops and strings in AdS(5)xS(5)

TL;DR

This paper resolves a previous discrepancy in matching the expectation value of circular Wilson loops in N=4 super Yang-Mills with string theory predictions by computing the ratio of partition functions and addressing normalization issues.

Contribution

It introduces a method to correctly normalize string path integrals by relating Wilson loop expectation values to zero mode contributions, achieving precise matching.

Findings

Resolved the normalization discrepancy in Wilson loop matching.

Computed the ratio of string partition functions for different Wilson loops.

Identified the role of zero modes in the normalization of string path integrals.

Abstract

Previous attempts to match the exact N=4 super Yang-Mills expression for the expectation value of the 1/2-BPS circular Wilson loop with the semiclassical AdS(5)xS(5) string theory prediction were not successful at the first subleading order. There was a missing prefactor ~ lambda^(-3/4) which could be attributed to the unknown normalization of the string path integral measure. Here we resolve this problem by computing the ratio of the string partition functions corresponding to the circular Wilson loop and the special 1/4-supersymmetric latitude Wilson loop. The fact that the latter has a trivial expectation value in the gauge theory allows us to relate the prefactor to the contribution of the three zero modes of the "transverse" fluctuation operator in the 5-sphere directions.