Klein Bottles and Simple Currents

TL;DR

This paper links Klein bottle coefficients in open string theories to Frobenius-Schur indicators, showing that non-standard Klein bottles correspond to simple currents, and proves positivity and integrality of string multiplicities.

Contribution

It establishes a connection between Klein bottle projections and simple currents, generalizing open string constructions to include non-standard Klein bottles using Frobenius-Schur indicators.

Findings

Klein bottle coefficient equals Frobenius-Schur indicator

Non-standard Klein bottles correspond to simple currents

Proved positivity and integrality of string multiplicities

Abstract

The standard Klein bottle coefficient in the construction of open descendants is shown to equal the Frobenius-Schur indicator of a conformal field theory. Other consistent Klein bottle projections are shown to correspond to simple currents. These observations enable us to generalize the standard open string construction from C-diagonal parent theories to include non-standard Klein bottles. Using (generalizations of) the Frobenius-Schur indicator we prove positivity and integrality of the resulting open and closed string state multiplicities for standard as well as non-standard Klein bottles.