Integers in the open string

TL;DR

This paper proves the integrality of certain quantities in rational conformal field theory and confirms a conjecture, highlighting unique features when the modular matrix T has odd order.

Contribution

It establishes the integrality of the $Y_{ab}^c$ in RCFT and proves a conjecture by Borisov-Halpern-Schweigert, with general applicability to theories with odd order T.

Findings

$Y_{ab}^c$ are integers in RCFT

Confirmed Borisov-Halpern-Schweigert conjecture

Identified special features for odd order T

Abstract

We show that the $Y_{ab}^c$ of Pradisi-Sagnotti-Stanev are indeed integers, and we prove a conjecture of Borisov-Halpern-Schweigert. We indicate some of the special features which arise when the order of the modular matrix T is odd. Our arguments are general, applying to arbitrary ``parent'' RCFT assuming only that T has odd order.