Contact Term Algebras and Dijkgraaf's Master Equation

TL;DR

This paper explores integrable deformations of chiral conformal field theories on elliptic curves using contact algebra, deriving contact relations and formulating Dijkgraaf's master equation for chiral deformations.

Contribution

It introduces a new integrable condition within conformal vertex algebra and rigorously formulates Dijkgraaf's master equation for chiral deformations.

Findings

Derived contact term relations among local operators.

Formulated three versions of genus one partition functions.

Established a rigorous framework for Dijkgraaf's master equation.

Abstract

This paper is devoted to study integrable deformations of chiral conformal field theories on elliptic curves from the viewpoint of contact algebra. We introduce the relevant integrable condition within the framework of conformal vertex algebra, and derive the contact term relations among certain local operators. We investigate three versions of genus one partition functions and derive the contact equations. This leads to a rigorous formulation of Dijkgraaf's master equation \cite{Dijk1996master} for chiral deformations.