  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.
