From Spinning Primaries to Permutation Orbifolds

TL;DR

This paper systematically analyzes primary operators in a free Weyl fermion conformal field theory, deriving counting formulas, dualities, and connections to permutation orbifolds with palindromic Hilbert series.

Contribution

It develops explicit counting formulas for primaries, establishes a duality map, and links primaries to polynomial functions on permutation orbifolds, advancing understanding of fermionic CFTs.

Findings

Derived explicit generating functions for primary operators.

Established a duality between primaries and polynomial functions.

Connected primaries to permutation orbifolds with palindromic Hilbert series.

Abstract

We carry out a systematic study of primary operators in the conformal field theory of a free Weyl fermion. Using SO(4,2) characters we develop counting formulas for primaries constructed using a fixed number of fermion fields. By specializing to particular classes of primaries, we derive very explicit formulas for the generating functions for the number of primaries in these classes. We present a duality map between primary operators in the fermion field theory and polynomial functions. This allows us to construct the primaries that were counted. Next we show that these classes of primary fields correspond to polynomial functions on certain permutation orbifolds. These orbifolds have palindromic Hilbert series.