Orbifolds from Modular Orbits

TL;DR

This paper introduces a novel method for constructing orbifolds in 2D conformal field theories using modular group orbits, ensuring modular invariance even in asymmetric cases and providing explicit spectrum constructions.

Contribution

It presents a new approach to orbifold construction via modular orbits, maintaining modular invariance and extending applicability to asymmetric and continuous symmetry cases.

Findings

Method always consistent for cyclic symmetries

Maintains manifest modular invariance

Explicit spectrum constructions for subgroup symmetries

Abstract

Given a two-dimensional conformal field theory with a global symmetry, we propose a method to implement an orbifold construction by taking orbits of the modular group. For the case of cyclic symmetries we find that this approach always seems to be consistent, even in asymmetric orbifold cases where the usual construction does not yield a modular invariant theory; our approach keeps modular invariance manifest but may give a result that is equivalent to the original theory. For the case that the symmetry is a subgroup of a continuous flavor symmetry, we can give explicit constructions of the spectrum, with twisted sectors corresponding to a non-standard group projection on an enlarged twisted sector Hilbert space.