Logarithmic intertwining operators and associative algebras

TL;DR

This paper demonstrates a fundamental connection between logarithmic intertwining operators in vertex operator algebras and module homomorphisms in a generalized Zhu's algebra, deepening understanding of algebraic structures in conformal field theory.

Contribution

It establishes an isomorphism linking logarithmic intertwining operators with module homomorphisms for a generalized Zhu's algebra, extending previous algebraic frameworks.

Findings

Proves an isomorphism between intertwining operators and algebra homomorphisms.

Connects vertex operator algebra theory with generalized Zhu's algebra.

Provides new tools for studying logarithmic modules in conformal field theory.

Abstract

We establish an isomorphism between the space of logarithmic intertwining operators among suitable generalized modules for a vertex operator algebra and the space of homomorphisms between suitable modules for a generalization of Zhu's algebra given by Dong-Li-Mason.