Energy-momentum tensors, supercurrents, (super)traces, and quantum equivalence

We show that although different field representations (e.g. representations of spin-zero particles by scalar and antisymmetric tensor fields) give rise to different trace anomalies in gravitational backgrounds, their quantum energy-momentum tensors and in particular their traces (total trace, i.e., anomalous+nonanomalous parts) are the same. For supersymmetric systems (e.g. representations of the scalar multiplet by chiral scalar or chiral spinor superfields) the quantum supercurrents and supertraces again are the same (and in particular the one-loop dsup(m)jsub(m)sup((5)), γxS, Tsub(m)sup(m) form a multiplet). (orig.)