NLL resummation for the static potential in N=4 SYM theory

TL;DR

This paper computes the next-to-leading logarithmic (NLL) resummation of the static potential in N=4 supersymmetric Yang-Mills theory, providing detailed anomalous dimensions and confirming previous fixed-order results.

Contribution

It presents the complete NLL running of the static potential in N=4 SYM, including two-loop calculations and explicit expressions for ladder and non-ladder diagram contributions.

Findings

Confirmed fixed-order results for the static potential at third order in the coupling.

Derived explicit anomalous dimensions for the static potential.

Provided expressions for non-ladder diagram contributions at NLL.

Abstract

We determine the complete NLL running of the static potential associated with the locally 1/2 BPS Wilson loop in N=4 supersymmetric Yang-Mills theory. We present results for the SU(N_c) singlet as well as for the adjoint configuration and arbitrary N_c at weak coupling. In order to derive the respective anomalous dimensions we perform a two-loop calculation in the N=4 supersymmetric version of the effective field theory pNRQCD. In addition we confirm the recently obtained fixed-order result for the singlet static potential generated exclusively by ladder diagrams to the third order in the t`Hooft coupling. We also give an explicit expression for the logarithmic contribution of all non-ladder diagrams at this order.