DECOUPLING IN NONPERTURBATIVE BACKGROUND FIELDS - THE THERMAL SPHALERON

Standard decoupling of heavy fermions may fail when there are nonpertu rbative variations in a scalar field which gives masses to the fermion s. One situation of phenomenological relevance is the case of sphalero ns in the presence of external fermions at finite temperatures. The fr ee energy of a simple model-is determined-using a nonperturbative tech nique to study the effect of fermions on the scalar field. The effects of quantum and thermal fermion fluctuations on the free energy of the sphaleron are calculated, including all orders in gradients of the sc alar field.