Finite Witt Jacobi cancellation

Abstract

Actual finite triple-c Witt cancellation

The formulas are the classical bc ghost BRST construction, with vacuum cuts b at minus one and c at two. See Kato and Ogawa, Nuclear Physics B 212 (1983), 443–460, and Polchinski, String Theory, volume 1, chapter 4. No novelty of these formulas is claimed. The formal carrier is the original complex finitely supported occupation space.

Theorem 1.1 (Qg R).

$$\forall r\in Int,\mathrm{Qg}\cdot R\left(r\right)-R\left(r\right)\cdot \mathrm{Qg}=0$$

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

Source. Repository-derived.

Commentary.

Expanding the actual quadratic Ward operator gives two jointly finite triple-c sums. Cyclic permutations of three actual c modes have positive sign, including repeated indices. A bijection on the two free integer indices identifies all cyclic sums. The polynomial (a-b)(a+b-c) plus its two cyclic permutations is zero, so the full operator sum vanishes.

This is an algebraic ghost-sector construction. It supplies a dependency for the broader Monster, vertex algebra, conformal field theory and string programme. It does not establish the matter-tensor BRST charge, its cohomology, a no-ghost theorem, string dynamics or AdS/CFT.

References

• Truth anchor: D5/S3/Quantum/Fermionic/BcGhostJacobi.Qg_R
• Dependency: D5/S3/Quantum/Fermionic/BcGhostBRST