Static Potential in N=4 Supersymmetric Yang-Mills Theory

TL;DR

This paper calculates the leading perturbative correction to the static potential in ${ m N}=4$ supersymmetric Yang-Mills theory, revealing infrared logarithms and their resummation, which aligns with strong coupling predictions from AdS/CFT.

Contribution

It provides the first perturbative analysis of the static potential in ${ m N}=4$ SYM, connecting weak and strong coupling behaviors through resummation techniques.

Findings

Infrared logarithms appear in the perturbative expansion.

Resummation of logs yields a coupling-dependent correction.

Strong coupling limit matches supergravity results.

Abstract

We compute the leading order perturbative correction to the static potential in ${\cal N}=4$ supersymmetric Yang-Mills theory. We show that the perturbative expansion contains infrared logarithms which, when resummed, become logarithms of the coupling constant. The resulting correction goes in the right direction to match the strong coupling behavior obtained from the AdS/CFT correspondence. We find that the strong coupling extrapolation of the sum of ladder diagrams goes as $\sqrt{g^2N}$, as in the supergravity approach.