What Maxwell Theory in D<>4 teaches us about scale and conformal invariance

TL;DR

The paper explores how free Maxwell theory in dimensions other than four exemplifies a scale invariant but non-conformally invariant quantum field theory, and how conformality can be restored by extending the operator content.

Contribution

It demonstrates the conditions under which Maxwell theory in D<>4 is scale invariant but not conformally invariant and shows how to restore conformality through operator extension.

Findings

Maxwell theory in D<>4 is scale invariant but not conformally invariant.

Restoring conformality involves adding local operators, which affects unitarity in higher dimensions.

The extended symmetry structure relates to the OSp(D,2|2) superalgebra.

Abstract

The free Maxwell theory in D<>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_mn 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|2) superalgebra.