Modular Orbits at Higher Genus

TL;DR

This paper generalizes the modular orbits method to higher genus Riemann surfaces, enabling the construction of partition functions and correlation functions for orbifold conformal field theories on complex surfaces.

Contribution

It introduces a straightforward generalization of the modular orbits method to higher genus, allowing explicit computation of partition functions and correlation functions in orbifold CFTs.

Findings

Partition functions on arbitrary genus surfaces can be systematically constructed.

Explicit results provided for symmetric and asymmetric orbifolds of free bosonic theories.

Method facilitates computation of OPE coefficients in higher genus contexts.

Abstract

We extend the modular orbits method of constructing a two-dimensional orbifold conformal field theory to higher genus Riemann surfaces. We find that partition functions on surfaces of arbitrary genus can be constructed by a straightforward generalization of the rules that one would apply to the torus. We demonstrate how one can use these higher genus objects to compute correlation functions and OPE coefficients in the underlying theory. In the case of orbifolds of free bosonic theories by subgroups of continuous symmetries, we can give the explicit results of our procedure for symmetric and asymmetric orbifolds by cyclic groups.