Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling

TL;DR

This paper calculates the 1-loop quantum correction to the string dual of a circular Wilson loop in AdS/CFT, using a method that simplifies fluctuation determinants and matches gauge theory results up to a factor.

Contribution

It introduces a general approach for regularizing fluctuation determinants in string solutions with factorized spectral problems, applicable to various boundary conditions and solutions.

Findings

1-loop partition function matches gauge theory expectations up to a factor

Method applicable to non-homogeneous open and closed string solutions

Discrepancy due to normalization of zero modes, not the core calculation

Abstract

We compute the 1-loop correction to the effective action for the string solution in AdS_5 x S^5 dual to the circular Wilson loop. More generically, the method we use can be applied whenever the two dimensional spectral problem factorizes, to regularize and define the fluctuation determinants in terms of solutions of one-dimensional differential equations. A such it can be applied to non-homogeneous solutions both for open and closed strings and to various boundary conditions. In the case of the circular Wilson loop, we obtain, for the 1-loop partition function a result which up to a factor of two matches the expectation from the exact gauge theory computation. The discrepancy can be attributed to an overall constant in the string partition function coming from the normalization of zero modes, which we have not fixed.