Open Descendants of Non-Diagonal Invariants

TL;DR

This paper constructs and analyzes open descendants of simple current automorphism invariants in conformal field theory, ensuring they meet key physical consistency conditions and exploring new Klein bottle projections.

Contribution

It provides a systematic construction of open descendants for non-diagonal invariants, proving their consistency and deriving new relations in the theory.

Findings

Solutions satisfy completeness, positivity, and integrality conditions

Derived new relations between tensor Y and fixed point CFT

Explored non-standard Klein bottle projections

Abstract

The open descendants of simple current automorphism invariants are constructed. We consider the case where the order of the current is two or odd. We prove that our solutions satisfy the completeness conditions, positivity and integrality of the open and closed sectors and the Klein bottle constraint (apart from an interesting exception). In order to do this, we derive some new relations between the tensor Y and the fixed point conformal field theory. Some non-standard Klein bottle projections are considered as well.