A formula for the partition function of the beta-gamma system on the cone pure spinors

TL;DR

This paper derives a closed-form formula for the partition function of the beta-gamma system on the cone of pure spinors, expressed through advanced mathematical functions like theta functions and Eisenstein series.

Contribution

It provides the first explicit closed-form expression for the partition function of this system, connecting it with special functions in mathematics.

Findings

Closed-form formula for the partition function $Z(t,q)$

Expression involves theta functions, $q$-Pochhammer symbols, and Eisenstein series

Enhances understanding of the beta-gamma system on pure spinor cones

Abstract

In this note, we propose a closed formula for the partition function $Z(t,q)$ of the $\beta\gamma$ system on the cone of pure spinors. We give the answer in terms of theta functions, $q$-Pochhammer symbols and Eisenstein series.