New dimensionally reduced effective action for QCD at high temperature.

New terms are derived for the three-dimensional effective action of the static modes of pure gauge SU(N) at high temperature. In previous works, effective vertices have been obtained by evaluating diagrams involving 2, 3 or 4 external static gluons with one internal nonstatic loop. I take a somewhat different approach by making a covariant derivative expansion of the one loop effective action for the static modes, keeping all terms involving up to six covariant derivatives. The resulting effective action is manifestly invariant under spatially dependent gauge transformations and contains new 5and 6-point effective vertices.