  In the deconfined regime of a non-Abelian gauge theory at nonzero
temperature, previously it was argued that if a (gauge invariant) source is
added to generate nonzero holonomy, that this source must be linear for small
holonomy. The simplest example of this is the second Bernoulli polynomial.
However, then there is a conundrum in computing the free energy to $\sim g^3$
in the coupling constant $g$, as part of the free energy is discontinuous as
the holonomy vanishes. In this paper we investigate two ways of generating the
second Bernoulli polynomial dynamically: as a mass derivative of an auxiliary
field, and from two dimensional ghosts embedded isotropically in four
dimensions. Computing the holonomous hard thermal loop (HHTL) in the gluon
self-energy, we find that the limit of small holonomy is only well behaved for
two dimensional ghosts, with a free energy which to $\sim g^3$ is continuous as
the holonomy vanishes.
