What Maxwell theory in d ≠ 4 teaches us about scale and conformal invariance

The free Maxwell theory in d not equal 4 dimensions provides a physical example of a unitary, scale invariant theory which is NOT conformally invariant. The easiest way to see this is that the field strength operator F-mu nu is neither a primary nor a descendant. We show how conformal multiplets can be completed, and conformality restored, by adding new local operators to the theory. In d >= 5, this can only be done by sacrificing unitarity of the extended Hilbert space. We analyze the full symmetry structure of the extended theory, which turns out to be related to the OSp(d, 2 vertical bar 2) superalgebra. (C) 2011 Elsevier B.V. All rights reserved.