Open Descendants in Conformal Field Theory

TL;DR

This paper develops a framework for constructing open descendants of Conformal Field Theory on unoriented surfaces with boundaries, introducing new algebraic structures to classify boundary operators in both diagonal and non-diagonal models.

Contribution

It introduces two types of generalized fusion tensors, one with signed integers for diagonal models and another with positive integers for non-diagonal models, advancing boundary operator classification.

Findings

New tensor with signed integers satisfying fusion algebra

New tensor with positive integers encoding boundary operator classification

Framework applicable to both diagonal and non-diagonal models

Abstract

Open descendants extend Conformal Field Theory to unoriented surfaces with boundaries. The construction rests on two types of generalizations of the fusion algebra. The first is needed even in the relatively simple case of diagonal models. It leads to a new tensor that satisfies the fusion algebra, but whose entries are signed integers. The second is needed when dealing with non-diagonal models, where Cardy's ansatz does not apply. It leads to a new tensor with positive integer entries, that satisfies a set of polynomial equations and encodes the classification of the allowed boundary operators.