Intertwiners in Orbifold Conformal Field Theories

TL;DR

This paper demonstrates the uniqueness and explicit description of intertwiners between twisted sectors in orbifold conformal field theories, providing a framework for verifying model consistency without detailed twisted sector structures.

Contribution

It establishes the uniqueness and explicit form of intertwiners in orbifold theories and proposes sufficiency conditions for consistency checks of such models.

Findings

Intertwiners between twisted sectors are unique and explicitly described.

Proposed sufficiency conditions for orbifold model consistency.

Application to a third order no-fixed-point lattice twist.

Abstract

Following on from earlier work relating modules of meromorphic bosonic conformal field theories to states representing solutions of certain simple equations inside the theories, we show, in the context of orbifold theories, that the intertwiners between twisted sectors are unique and described explicitly in terms of the states corresponding to the relevant modules. No explicit knowledge of the structure of the twisted sectors is required. Further, we propose a general set of sufficiency conditions, illustrated in the context of a third order no-fixed-point twist of a lattice theory, for verifying consistency of arbitrary orbifold models in terms of the states representing the twisted sectors.