Six-dimensional Methods for Four-dimensional Conformal Field Theories II: Irreducible Fields

Abstract

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 $\epsilon_{\mu\nu\rho\sigma}$.