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Ghost degree of the original cubic charge

Abstract

Ghost degree of the original cubic charge

The number operator is the original locally finite bc ghost-number operator. The cubic is normally ordered with the original b and c vacuum cuts; no intercept is added.

Theorem 1.1 (The cubic has ghost degree one).

Lean statement: D5/S3/Quantum/Fermionic/BcGhostBRSTDegree.ghost_number_Qg

Proof. Machine-checked in Lean as D5/S3/Quantum/Fermionic/BcGhostBRSTDegree.ghost_number_Qg (✓ std3). ∎

Source. Repository-derived.

Commentary.

On the original complex countable occupation Fock space, ghostNumber * Qg - Qg * ghostNumber = Qg. Each normally ordered cubic has two c factors of degree one and one b factor of degree minus one. The commutator passes through the statewise finite cubic sums, using finite support at both v and ghostNumber v.

This algebraic result is a step toward the Monster, VOA/CFT, anomaly and fusion programme. BRST cohomology, the no-ghost theorem, a physical string model and an AdS/CFT correspondence require further constructions.

References