GAUGE FIELD IMPROVEMENT, FORM-SCALAR DUALITY, CONFORMAL-INVARIANCE AND QUASI-LOCALITY

The problem of maintaining scale and conformal invariance in Maxwell a nd general N-form gauge theories away from their critical dimension d( c) = 2(N + 1) is analyzed. We first exhibit the underlying group-theor etical clash between locality, gauge, Lorentz and conformal invariance requirements. ''Improved''-traceless-stress tensors are then construc ted; each violates one of the above criteria. However, when d = N + 2, there is a duality equivalence between N-form models and massless sca lars in d = N + 2. Here we show that N-form conformal invariance is no t lost, by constructing a quasilocal gauge invariant improved stress t ensor. The correlators of the scalar theory are then reproduced, inclu ding the latter's trace anomaly. This resolves the old conformal invar iance ''paradox'' between the dual partners.