Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras

TL;DR

This paper establishes the existence and associativity of the nonmeromorphic operator product expansion for triplet W-algebras and proves their C_2-cofiniteness, advancing the understanding of their algebraic structure.

Contribution

It introduces a proof of the nonmeromorphic operator product expansion and C_2-cofiniteness for an infinite family of W-algebras, using P(z)-tensor product theory.

Findings

Proved the existence of nonmeromorphic OPE for triplet W-algebras

Established associativity of the operator product expansion

Showed all these W-algebras are C_2-cofinite

Abstract

We prove the existence and associativity of the nonmeromorphic operator product expansion for an infinite family of vertex operator algebras, the triplet W-algebras, using results from P(z)-tensor product theory. While doing this, we also show that all these vertex operator algebras are C_2-cofinite.