Crosscaps in Gepner Models and Type IIA Orientifolds

TL;DR

This paper constructs crosscap states in Gepner models related to Calabi-Yau manifolds and explores their duality with M-theory compactifications on G2 holonomy manifolds, focusing on orientifolds with anti-holomorphic involutions.

Contribution

It introduces a method to construct crosscap states in Gepner models for Calabi-Yau orientifolds and discusses their duality with M-theory on G2 manifolds, advancing understanding of string/M-theory dualities.

Findings

Constructed crosscap states for Calabi-Yau orientifolds.

Established duality between Gepner model orientifolds and M-theory on G2 manifolds.

Analyzed the case of the quintic Calabi-Yau.

Abstract

As a first step to a detailed study of orientifolds of Gepner models associated with Calabi-Yau manifolds, we construct crosscap states associated with anti-holomorphic involutions (with fixed points) of Calabi-Yau manifolds. We argue that these orientifolds are dual to M-theory compactifications on (singular) seven-manifolds with $G_2$ holonomy. Using the spacetime picture as well as the M-theory dual, we discuss aspects of the orientifold that should be obtained in the Gepner model. This is illustrated for the case of the quintic.