Beta-gamma system, pure spinors and Hilbert series of arc spaces

TL;DR

This paper develops algorithms to compute the partition function of constrained beta-gamma systems using Hilbert series of arc spaces, with applications to complex surfaces and pure spinors, enhancing computational methods in string theory.

Contribution

It introduces algorithms linking partition functions to Hilbert series of arc spaces, providing new computational tools for constrained beta-gamma systems and pure spinors.

Findings

Algorithms successfully compute partition functions for specific systems.

Results agree with existing calculations for known models.

Method extends to complex algebraic varieties with singularities.

Abstract

Algorithms are presented for calculating the partition function of constrained beta-gamma systems in terms of the generating functions of the individual fields of the theory, the latter obtained as the Hilbert series of the arc space of the algebraic variety defined by the constraint. Examples of a beta-gamma system on a complex surface with an $A_1$ singularity and pure spinors are worked out and compared with existing results.