Holomorphic primary fields in free CFT4 and Calabi-Yau orbifolds

Understand

Counting formulae for general primary fields in free four dimensional conformal field theories of scalars, vectors and matrices are derived.

• These are specialised to count primaries which obey extremality conditions defined in terms of the dimensions and left or right spins (i.e.
• in terms of relations between the charges under the Cartan subgroup of $SO(4,2)$).
• The construction of primary fields for scalar field theory is mapped to a problem of determining multi-variable polynomials subject to a system of symmetry and differential constraints.