Conformal primary operator

A conformal primary operator is annihilated at the origin by every special conformal generator. Acting with translation generators produces its conformal descendants.

A scalar primary operator transforms without a spin rotation and is characterized by its scaling dimension. Conformal symmetry fixes its two- and three-point functions up to constants, while a four-point function can depend on conformal cross-ratios.

A conformal descendant is obtained by applying one or more translation generators to a conformal primary operator. Its scaling dimension exceeds that of the primary by a nonnegative integer.

Positivity of descendant norms constrains the scaling dimension of a primary operator. For a nonidentity scalar primary in $d\ge 2$, unitarity requires $\Delta \ge (d-2)/2$.