Orbifolds from Modular Orbits

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.

arXiv comment44 pages, minor typos corrected

References in corpus (14)

• Generalized Global Symmetries
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• On gauging finite subgroups
• The "Parity" Anomaly On An Unorientable Manifold
• Cluster decomposition, T-duality, and gerby CFT's
• Systematic approach to cyclic orbifolds
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• Anomalies and Bounds on Charged Operators
• Notes on gauging noneffective group actions
• Constraints on Flavored 2d CFT Partition Functions
• Worldsheet CFTs for Flat Monodrofolds
• On the Construction of Asymmetric Orbifold Models
• Black Holes, Black Rings and their Microstates
• An Uplifting Discussion of T-Duality

Cited by in corpus (10)

• Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases
• Anomaly resolution via decomposition
• Quantum symmetries in orbifolds and decomposition
• Non-Supersymmetric AdS from String Theory
• A generalization of decomposition in orbifolds
• Anomalies, Extensions and Orbifolds
• Bootstrapping Lieb-Schultz-Mattis anomalies
• Flat equivariant gerbes: holonomies and dualities
• Modular Orbits at Higher Genus
• Shift orbifolds, decompactification limits, and lattices