The Heisenberg Generalized Vertex Operator Algebra on a Riemann Surface

TL;DR

This paper computes partition and correlation functions for the Heisenberg generalized vertex operator algebra on a genus g Riemann surface, using combinatorial methods and advanced mathematical tools.

Contribution

It provides explicit formulas for these functions on higher-genus surfaces, extending previous work to more complex geometric settings.

Findings

Explicit expressions for partition functions on genus g surfaces

Use of combinatorial methods and MacMahon Master Theorem generalization

Connections to differential forms and period matrices

Abstract

We compute the partition and correlation generating functions for the Heisenberg intertwiner generalized vertex operator algebra on a genus $g$ Riemann surface in the Schottky uniformization. These are expressed in terms of differential forms of the first, second and third kind, the prime form and the period matrix and are computed by combinatorial methods using a generalization of the MacMahon Master Theorem.