On Orientifolds of c=1 Orbifolds

TL;DR

This paper systematically analyzes orientifold projections in c=1 orbifold conformal field theories, comparing rational and fractional radius cases, and confirms consistency across various modular invariants.

Contribution

It provides a comprehensive classification of orientifold projections for c=1 orbifolds and verifies their consistency with known Klein bottle amplitudes at rational and fractional radii.

Findings

Klein bottle amplitudes match proposed orientifold projections at rational points.

Exceptional modular invariants are consistent with the orientifold projections.

The analysis extends to fractional square radius theories, confirming their consistency.

Abstract

The aim of this paper is to study orientifolds of c=1 conformal field theories. A systematic analysis of the allowed orientifold projections for c=1 orbifold conformal field theories is given. We compare the Klein bottle amplitudes obtained at rational points with the orientifold projections that we claim to be consistent for any value of the orbifold radius. We show that the recently obtained Klein bottle amplitudes corresponding to exceptional modular invariants, describing bosonic string theories at fractional square radius, are also in agreement with those orientifold projections.