Transition from weak to strong coupling in thermal gauge theories: Lessons from ${\cal N}=4$ SYM Theory

TL;DR

This paper studies the transition from weak to strong coupling in thermal ${ m f N}=4$ SYM theory by interpolating between known perturbative and holographic results using Padé approximants, revealing the transition's characteristics.

Contribution

It introduces a method to interpolate between weak and strong coupling regimes in thermal ${ m f N}=4$ SYM using Padé approximants, providing insights into the transition.

Findings

Identifies the coupling range where the transition occurs.

Determines the width of the transition region.

Provides a quantitative interpolation between regimes.

Abstract

We investigate the transition between weak and strong coupling in thermal ${\cal N}=4$ supersymmetric Yang-Mills (SYM) theory as a function of 't Hooft coupling $\lambda$ for several quantities of phenomenological interest for which next-to-leading order calculations are available in both regimes. We use Pad\'e approximants to interpolate between the weak and strong coupling expansions and determine the location and width of the transition between the asymptotic regimes.