Genus Two Virasoro Correlation Functions for Vertex Operator Algebras

TL;DR

This paper develops explicit generating functions for genus two correlation functions of Virasoro vacuum descendants in vertex operator algebras, utilizing differential operators and Siegel modular group actions.

Contribution

It introduces a novel combinatorial and analytical framework for expressing genus two correlation functions in terms of differential operators and modular group symmetries.

Findings

Explicit generating functions for genus two correlation functions

Connection to Siegel modular group actions

Framework applicable to Virasoro vacuum descendants

Abstract

We consider all genus two correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially expressed in terms of a sequence of globally defined differential operators on which the genus two Siegel modular group $Sp(4,\mathbb{Z})$ has a natural action.