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

TL;DR

The paper computes the subleading term κ in the strong-coupling expansion of the heavy-quark potential in N=4 SYM at zero temperature using AdS/CFT. It derives κ from the one-loop effective action of string worldsheet fluctuations around the minimal surface, separating spectral and measure contributions and evaluating the resulting determinant ratios numerically. The main result is κ ≈ -1.33460, with κ2 vanishing due to conformal-measure cancellations, leading to V(r) = -a(λ)/r with a(λ) = [4π^2/Γ^4(1/4)]√λ[1 - 1.33460/√λ + O(1/λ)]. The work provides a robust next-to-leading correction to the leading √λ behavior and discusses gauge considerations and extensions to finite temperature.

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.

Figures (2)

• Figure 1: the top curve represents $\hat{C}_3(\omega)$, the middle one represents $\hat{C}_1(\omega)$, the bottom one represents $\hat{C}_2(\omega)$.
• Figure 2: the left curve represents $\rho(\omega)$, while the right one represents $\rho^{\rm{sol.}}(\omega)$.