Logarithmic intertwining operators and the space of conformal blocks over the projective line

TL;DR

This paper establishes an isomorphism between the space of logarithmic intertwining operators for vertex operator algebras and the space of 3-point conformal blocks on the projective line, generalizing Zhu's classical result.

Contribution

It extends Zhu's theorem to logarithmic modules, connecting intertwining operators with conformal blocks in a broader setting.

Findings

Isomorphism between logarithmic intertwining operators and conformal blocks

Generalization of Zhu's result to logarithmic modules

Framework for studying logarithmic conformal field theories

Abstract

We show that the space of logarithmic intertwining operators among logarithmic modules for a vertex operator algebra is isomorphic to the space of 3-point conformal blocks over the projective line. This is considered as a generalization of Zhu's result for ordinary intertwining operators among ordinary modules.