Virasoro Correlation Functions for Vertex Operator Algebras

TL;DR

This paper provides explicit combinatorial formulas for genus zero and one correlation functions of Virasoro vacuum descendants in vertex operator algebras, linking them to graph theory concepts like derangements and partial permutations.

Contribution

It introduces a novel combinatorial framework to compute Virasoro correlation functions at genus zero and one, connecting algebraic structures to graph theory.

Findings

Correlation functions expressed via generating functions

Graph-theoretic combinatorial descriptions established

Explicit formulas for genus zero and one cases

Abstract

We consider all genus zero and genus one 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 graph theory related to derangements in the genus zero case and to partial permutations in the genus one case.