Asymptotic Freedom and Compositeness

TL;DR

This paper analyzes a composite field in SU(2) Yang-Mills theory at high temperatures, revealing its role in ground-state structure and infrared problem resolution despite strong suppression.

Contribution

It introduces a detailed computation of a composite field's phase and modulus, highlighting its nontrivial topology and physical relevance at high temperatures.

Findings

The composite field exhibits nontrivial $S^1$-winding on $S^3$.

The field remains relevant at high temperatures despite power suppression.

Its presence addresses the infrared issues in thermal perturbation theory.

Abstract

We compute the phase and the modulus of an energy- and pressure-free, composite, adjoint, and inert field $\phi$ in an SU(2) Yang-Mills theory at large temperatures. This field is physically relevant in describing part of the ground-state structure and the quasiparticle masses of excitations. The field $\phi$ possesses nontrivial $S^1$-winding on the group manifold $S^3$. Even at asymptotically high temperatures, where the theory reaches its Stefan-Boltzmann limit, the field $\phi$, though strongly power-suppressed, is conceptually relevant: its presence resolves the infrared problem of thermal perturbation theory.