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

By S. El-Showk, Y. Nakayama, S. Rychkov. 2011

141 citations recorded by the source corpus.

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_(μν) 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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4a92a981482206671009289932837ef8c086ca14

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In Geometry and Topology

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Citations in the corpus

Operator bases, S-matrices, and their partition functions (2017, background): “See [53] for a related discussion concerning Maxwell theory outside four dimensions.”
Deformations of superconformal theories (2016, background): “For instance, this happens on the Coulomb branches of maximally supersymmetric YangMills theories in d ≥ 5, because free vector fields in these dimensions are not conformally invariant (see for instance [63]).”
Conformal invariance in the long-range Ising model (2015, background): “As is well known, such a vector theory without gauge invariance (“theory of elasticity”) is not conformally invariant [75, 53].”