BPS orientifold planes from crosscap states in Calabi-Yau compactifications

TL;DR

This paper constructs BPS orientifold planes in Calabi-Yau compactifications using crosscap states derived from rational conformal field theory, ensuring they satisfy BPS-like relations and identifying their phases with automorphism types.

Contribution

It introduces a method to construct BPS orientifold planes in Calabi-Yau compactifications via crosscap states, extending previous classifications to include BPS conditions.

Findings

Derived crosscap states in Gepner models with odd k_i.

Confirmed BPS-like relation M=exp(i*phi)Q for orientifold planes.

Identified BPS phase phi with automorphism type of crosscap states.

Abstract

We use the results of hep-th/0007174 on the simple current classification of open unoriented CFTs to construct half supersymmetry preserving crosscap states for rational Calabi-Yau compactifications. We show that the corresponding orientifold fixed planes obey the BPS-like relation M=exp(i*phi)Q. To prove this relation, it is essential that the worldsheet CFT properly includes the degrees of freedom from the uncompactified space-time component. The BPS-phase phi can be identified with the automorphism type of the crosscap states. To illustrate the method we compute crosscap states in Gepner models with each k_i odd.