The Rank four Heterotic Modular Invariant Partition Functions

TL;DR

This paper develops techniques to classify heterotic modular invariants in conformal field theories, identifying all such invariants of rank four and extending the classification of related models.

Contribution

It introduces new methods for analyzing heterotic modular invariants and provides a complete classification for rank four cases, including previously unknown invariants.

Findings

Seven heterotic rank four invariants identified, two are new.

Complete classification of certain $su(2)$ product models.

Extended the classification beyond rank three cases.

Abstract

In this paper, we develop several general techniques to investigate modular invariants of conformal field theories whose algebras of the holomorphic and anti-holomorphic sectors are different. As an application, we find all such ``heterotic'' WZNW physical invariants of (horizontal) rank four: there are exactly seven of these, two of which seem to be new. Previously, only those of rank $\le 3$ have been completely classified. We also find all physical modular invariants for $su(2)_{k_1}\times su(2)_{k_2}$, for $22>k_1>k_2$, and $k_1=28$, $k_2<22$, completing the classification of ref.{} \SUSU.