QCD at complex coupling, large order in perturbation theory and the gluon condensate

TL;DR

This paper explores the large order behavior of perturbative series in pure gauge theory, its relation to complex coupling singularities, and implications for estimating the gluon condensate, supported by numerical analysis of Fisher's zeros and density of states.

Contribution

It introduces new extrapolation methods for perturbative series and investigates the complex coupling plane to better understand the gluon condensate and phase structure in gauge theories.

Findings

Large order series extrapolations suggest higher gluon condensate estimates.

Weak and strong coupling density of states expansions agree well in the crossover regime.

Numerical analysis of Fisher's zeros provides insights into phase transitions.

Abstract

We discuss the relationship between the large order behavior of the perturbative series for the average plaquette in pure gauge theory and singularities in the complex coupling plane. We discuss simple extrapolations of the large order for this series. We point out that when these extrapolated series are subtracted from the Monte Carlo data, one obtains (naive) estimates of the gluon condensate that are significantly larger than values commonly used in the continuum for phenomelogical purpose. We present numerical results concerning the zeros of the partition function in the complex coupling plane (Fisher's zeros). We report recent attempts to solve this problem using the density of states. We show that weak and strong coupling expansions for the density of states agree surprisingly well for values of the action relevant for the crossover regime.