The static potential in {\cal N}=4 supersymmetric Yang-Mills at weak coupling

TL;DR

This paper calculates the static potential in N=4 supersymmetric Yang-Mills theory at weak coupling, including resummation of leading logarithms, using an effective theory for ultrasoft degrees of freedom, and extends the analysis to ordinary Wilson loops.

Contribution

It develops an effective theory for ultrasoft modes up to next-to-leading order and computes the static potential with logarithmic resummation in N=4 SYM.

Findings

Computed the static potential at order λ^2/r

Resummed leading logarithms of order λ^{n+1} ln^n λ/r

Extended the formalism to ordinary Wilson loops

Abstract

We compute the static potential associated to the locally 1/2 BPS Wilson loop in ${\cal N}$=4 supersymmetric Yang-Mills theory with ${\cal O}(\lambda^2/r)$ accuracy. We also resum the leading logarithms, of ${\cal O}(\lambda^{n+1}\ln^n\lambda/r)$, and show the structure of the renormalization group equation at next-to-leading order in the multipole expansion. In order to obtain these results it is crucial the use of an effective theory for the ultrasoft degrees of freedom. We develop this theory up to next-to-leading order in the multipole expansion. Using the same formalism we also compute the leading logarithms, of ${\cal O}(\lambda^{n+3}\ln^n\lambda/r)$, of the static potential associated to an ordinary Wilson loop in the same theory.