Crosscaps, Boundaries and T-Duality

TL;DR

This paper investigates open string descendants with boundaries and crosscaps in Z_2 orbifold models, deriving unique crosscaps and Klein bottles, and uses T-duality to construct symmetry-preserving configurations.

Contribution

It introduces a method to determine unique crosscaps and Klein bottles in Z_2 orbifolds and applies T-duality to construct symmetry-preserving open string models.

Findings

Derived a unique crosscap of automorphism type g in Z_2 orbifolds.

Constructed g-twisted Klein bottles consistent with charge conjugation invariance.

Used T-duality to generate descendants of diagonal invariants with preserved symmetry.

Abstract

Open descendants with boundaries and crosscaps of non-trivial automorphism type are studied. We focus on the case where the bulk symmetry is broken to a Z_2 orbifold subalgebra. By requiring positivity and integrality for the open sector, we derive a unique crosscap of automorphism type g \in Z_2 and a corresponding g-twisted Klein bottle for a charge conjugation invariant. As a specific example, we use T-duality to construct the descendants of the true diagonal invariant with symmetry preserving crosscaps and boundaries.