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

Understand

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