Free quantum fields in 4D and Calabi-Yau spaces

Abstract

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. This sector includes and extends previous constructions of infinite families of primary fields. We sketch the generalization of these results to free 4D vector and matrix CFTs.

arXiv comment6 pages

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Cited by in corpus (5)

• Free field primaries in general dimensions: Counting and construction with rings and modules
• Moduli space of logarithmic states in critical massive gravities
• From Spinning Primaries to Permutation Orbifolds
• $\mathcal{N}=4$ SYM, (super)-polynomial rings and emergent quantum mechanical symmetries
• Perturbative 4D conformal field theories and representation theory of diagram algebras