The orbifold transform and its applications

TL;DR

This paper introduces the orbifold transform, explores its properties, and demonstrates its applications in permutation orbifolds and torus partition functions, providing a mathematical framework for analyzing symmetric products.

Contribution

It formalizes the orbifold transform, detailing its properties and illustrating its applications in permutation orbifolds and partition functions, advancing the mathematical understanding of these structures.

Findings

Orbifold transform exhibits transitivity and an exponential formula.

Connection established between orbifold transform and permutation orbifolds.

Applications demonstrated on torus partition functions.

Abstract

We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the theory of permutation orbifolds is addressed, and the general results illustrated on the example of torus partition functions.