Towards Vertex Algebras of Krichever-Novikov Type, Part I

TL;DR

This paper explores the construction of vertex algebra-like structures from Krichever-Novikov algebras, proposing a new definition of Krichever-Novikov type vertex algebras and analyzing their relation to classical vertex algebras.

Contribution

It introduces a novel class of vertex algebras based on Krichever-Novikov algebras and discusses their connection to traditional vertex algebra theory.

Findings

A representation of the Krichever-Novikov algebra yields a state field correspondence similar to classical vertex algebras.

A new definition of Krichever-Novikov type vertex algebras is proposed.

The relation between Krichever-Novikov type vertex algebras and standard vertex algebras is analyzed.

Abstract

It is shown that a certain representation of the Heisenberg type Krichever-Novikov algebra gives rise to a state field correspondence that is quite similar to the vertex algebra structure of the usual Heisenberg algebra. Finally a definition of Krichever-Novikov type vertex algebras is proposed and its relation to vertex algebras is discussed.