Perturbation theory for non-abelian gauge theories at finite temperature is
plagued by infrared divergences which are caused by magnetic soft modes ~g^2T,
corresponding to gluon fields of a 3d Yang-Mills theory. While the divergences
can be regulated by a dynamically generated magnetic mass on that scale, the
gauge coupling drops out of the effective expansion parameter requiring
summation of all loop orders for the calculation of observables. Some gauge
invariant possibilities to implement such infrared-safe resummations are
reviewed. We use a scheme based on the non-linear sigma model to estimate some
of the contributions ~g^6 of the soft magnetic modes to the QCD pressure
through two loops. The NLO contribution amounts to ~10% of the LO, suggestive
of a reasonable convergence of the series.Comment: 10 p.,Latex error fixed, Invited talk at International Workshop on
QCD Green's Functions, Confinement and Phenomenology (QCD-TNT09), Trento,
Italy, 7-11 Septembe
