The Subleading Term of the Strong Coupling Expansion of the Heavy-Quark Potential in a $\mathcal N=4$ Super Yang-Mills Vacuum

TL;DR

This paper calculates the sub-leading correction to the heavy-quark potential in N=4 super Yang-Mills theory at strong coupling using AdS/CFT, involving functional determinants of string fluctuations.

Contribution

It provides the first explicit computation of the sub-leading term in the strong coupling expansion of the heavy-quark potential via semi-classical string analysis.

Findings

Numerical evaluation of fluctuation determinants

Identification of singularities in the determinants

Quantitative correction to the heavy-quark potential

Abstract

Applying the AdS/CFT correspondence, the expansion of the heavy-quark potential of the ${\cal N}=4$ supersymmetric Yang-Mills theory at large $N_c$ is carried out to the sub-leading term in the large 't Hooft coupling at zero temperature. The strong coupling corresponds to the semi-classical expansion of the string-sigma model, the gravity dual of the Wilson loop operator, with the sub-leading term expressed in terms of functional determinants of fluctuations. The singularities of these determinants are examined and their contributions are evaluated numerically.