Free quantum fields in 4D and Calabi-Yau spaces

Understand

We develop general counting formulae for primary fields in free four dimensional (4D) scalar conformal field theory (CFT).

• Using a duality map between primary operators in scalar field theory and multi-variable polynomial functions subject to differential constraints, we identify a sector of holomorphic primary fields corresponding to polynomial functions on a class of permutation orbifolds.
• These orbifolds have palindromic Hilbert series, which indicates they are Calabi-Yau.
• We construct the top-dimensional holomorphic form expected from the Calabi-Yau property.