Systematic approach to cyclic orbifolds

TL;DR

The paper develops a systematic orbifold induction framework to construct cyclic orbifolds and their twisted sectors, introducing orbifold algebras as root-covering structures that mirror mother CFT constructions across affine, Virasoro, N=1/N=2, and W3 sectors. It provides explicit induction rules that map mother primary fields to orbifold counterparts, derives principal primaries and their correlators on the sphere, and formulates the local stress tensor, Ward identities, and null-state equations in the twisted sectors. The authors extend the analysis to torus characters, modular transformations, and fusion rules, offering detailed results for λ=2 and general λ, and verify consistency with known partition functions (e.g., Ising) and Verlinde fusion. The work also discusses fixed-point challenges, higher-twist copies, and potential generalizations to non-abelian permutation orbifolds and broader coset/affine-Virasoro constructions, highlighting the broad applicability of the orbifold induction approach in CFT.

Abstract

We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions of conformal field theory and enables us to find the orbifold characters and their modular transformation properties.