Gauge Field Improvement, Form-Scalar Duality and Conformal Invariance and Quasi-locality

The problem of maintaining scale and conformal invariance in Maxwell and general N form gauge theories away from their critical dimension d_c = 2(N + 1) is analyzed. We first exhibit the underlying group-theoretical clash between locality, gauge, Lorentz and conformal invariance requirements. "Improved"-traceless-stress tensors are then constructed; each violates one of the above criteria. However, when d = N + 2, there is a duality equivalence between N-form models and massless scalars in d = N + 2. Here we show that N-form conformal invariance is not lost, by constructing a quasilocal gauge invariant improved stress tensor. The correlators of the scalar theory are then reproduced, including the latter's trace anomaly. This resolves the old conformal invariance "paradox" between the dual partners.