This note supplements an earlier paper on conformal field theories. There it was shown how to construct tensor, spinor, and spinor-tensor primary fields in four dimensions from their counterparts in six dimensions, where conformal transformations act simply as $SO(4,2)$ Lorentz transformations. Here we show how to constrain fields in six dimensions so that the corresponding primary fields in four dimensions transform according to irreducible representations of the four-dimensional Lorentz group, even when the irreducibility conditions on these representations involve the four-component Levi-Civita tensor ${ϵ}_{\mu \nu \rho \sigma }$.

• Received 7 September 2012

DOI:https://doi.org/10.1103/PhysRevD.86.085013