Foliation of a space associated to vertex operator algebra

TL;DR

This paper constructs a foliation on a space linked to vertex operator algebra correlation functions on Riemann surfaces, providing a geometric framework for understanding these functions across different genera.

Contribution

It introduces a novel foliation structure on the space of correlation functions associated with vertex operator algebras on Riemann surfaces, extending the geometric understanding of these functions.

Findings

Constructed a foliation on the space of correlation functions.

Proved that genus g correlation functions determine this foliation.

Proposed applications of the foliation framework.

Abstract

We construct the foliation of aspace associated to correlation functions of vertex operator algebras on considered on Riemann surfaces. We prove that the computation of general genus $g$ correlation functions determines a foliation on the space associated to these correlation functions a sewn Riemann surface. Certain further applications of the definition are proposed.