Conformal Orbifold Partition Functions from Topologically Massive Gauge Theory

TL;DR

This paper develops a topological membrane approach to compute orbifold partition functions in open and unoriented string theories using three-dimensional gauge theory, reproducing known string sectors and modular invariants.

Contribution

It introduces a method to derive orbifold partition functions from topologically massive gauge theory, extending the topological membrane approach to orbifolds and open strings.

Findings

Reproduces twisted and untwisted sectors in orbifold string theories

Constructs characters of extended Kac-Moody groups for arbitrary genus

Produces modular invariant sums over characters in the gauge theory framework

Abstract

We continue the development of the topological membrane approach to open and unoriented string theories. We study orbifolds of topologically massive gauge theory defined on the geometry $[0,1]\times\Sigma$, where $\Sigma$ is a generic compact Riemann surface. The orbifold operations are constructed by gauging the discrete symmetries of the bulk three-dimensional field theory. Multi-loop bosonic string vacuum amplitudes are thereby computed as bulk correlation functions of the gauge theory. It is shown that the three-dimensional correlators naturally reproduce twisted and untwisted sectors in the case of closed worldsheet orbifolds, and Neumann and Dirichlet boundary conditions in the case of open ones. The bulk wavefunctions are used to explicitly construct the characters of the underlying extended Kac-Moody group for arbitrary genus. The correlators for both the original theory and its orbifolds give the expected modular invariant statistical sums over the characters.