On the structure of unoriented topological conformal field theories

TL;DR

This paper classifies open Klein topological conformal field theories using Calabi-Yau $A_ $-categories with involution, and explores their open-closed extensions related to involutive Hochschild chains.

Contribution

It provides a new classification framework for open Klein topological conformal field theories via Calabi-Yau $A_ $-categories with involution, including their universal open-closed extensions.

Findings

Classification of open Klein topological conformal field theories

Construction of universal open-closed extensions

Relation to involutive Hochschild chains

Abstract

We give a classification of open Klein topological conformal field theories in terms of Calabi-Yau $A_\infty$-categories endowed with an involution. Given an open Klein topological conformal field theory, there is a universal open-closed extension whose closed part is the involutive variant of the Hochschild chains of the open part.