Cauchy conformal fields in dimensions d>2

Understand

Holomorphic fields play an important role in 2d conformal field theory.

• We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined everywhere once we know their value on a codimension 1 surface.
• We classify all the unitary Cauchy fields.
• By analyzing the mode expansion on the unit sphere, we show that all unitary Cauchy fields are free in the sense that their correlation functions factorize on the 2-point function.