Scalar Duality , 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. 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.