Partition function of beta-gamma system on orbifolds

TL;DR

This paper computes the partition functions of beta-gamma systems on orbifolds C^2/Z_N and C^3/Z_M x Z_N by leveraging group actions and contour integration, resulting in series that count invariant monomials at each mass level.

Contribution

It introduces a method to derive the partition function on orbifolds by lifting geometric actions and interpreting sums over roots of unity as contour integrals, providing explicit series expressions.

Findings

Partition functions expressed as invariant series

Counting of invariant monomials at each mass level

Method applicable to specific orbifolds

Abstract

Partition function of beta-gamma systems on the orbifolds C^2/Z_N and C^3/Z_M x Z_N are obtained as the invariant part of that on the respective affine spaces, by lifting the geometric action of the orbifold group to the fields. Interpreting the sum over roots of unity as an elementary contour integration, the partition function evaluates to an infinite series counting invariant monomials composed of basic operators of the theory at each mass level.