Breakdown of unitarity in the dimensional reduction scheme

Abstract

B-functions of any field theory using different regularization schemes should obey the physical rule that they can be transformed into each other by a finite transformation of the renormalized coupling constants in the theory. The dimensional reduction scheme does not obey this rule. The cause is that unacceptable counterterms had to be used where overlapping divergencies occur, so that unitarity is violated. Supersymmetry (or at least the N = 2 and N = 4 supersymmetric gauge theories and all supersymmetric theories not containing a vector field) turns out to be insensitive to this discrepancy, because the so-called '-scalar' renormalizes the same way as the scalar, fermion and vector fields.