Yang-Mills thermodynamics at low temperature

TL;DR

This paper investigates the mathematical properties of the pressure series in SU(2) Yang-Mills thermodynamics at low temperatures, revealing Borel summability and complex behavior indicating turbulence phenomena.

Contribution

It demonstrates Borel summability of the pressure series in the confining phase and analyzes its analytic structure, linking mathematical properties to physical turbulence effects.

Findings

Pressure series is Borel summable for negative coupling.

The inverse Borel transform is meromorphic with a branch cut.

Physical pressure is zero at zero temperature and shows turbulence signatures.

Abstract

For the confining phase of SU(2) Yang-Mills thermodynamics we show that the asymptotic series representing the pressure is Borel summable for negative (unphysical) values of a suitably defined coupling constant. The inverse Borel transform is meromorphic except for a branch cut along the positive-real axis. The physical pressure is precisely nil at vanishing and acquires a small imaginary admixture at small temperature the latter indicating violations of thermal equilibrium (turbulences).