FC sets and twisters: the basics of orbifold deconstruction

TL;DR

This paper explores the properties of twisters and FC sets in orbifold deconstruction, providing tools to identify if a conformal model is an orbifold of another and to determine the twist group and original model.

Contribution

It introduces a detailed analysis of twisters and FC sets, enhancing the understanding of orbifold deconstruction in conformal field theory.

Findings

Character theory analogy with finite groups explained

Criteria for recognizing orbifold models developed

Methods to identify twist groups and original models

Abstract

We present a detailed account of the properties of twisters and their generalizations, FC sets, which are essential ingredients of the orbifold deconstruction procedure aimed at recognizing whether a given conformal model may be obtained as an orbifold of another one, and if so, to identify the twist group and the original model. The close analogy with the character theory of finite groups is discussed, and its origin explained.