Partition Functions for Heterotic WZW Conformal Field Theories

TL;DR

This paper explores the classification of heterotic conformal field theory partition functions with asymmetric algebra and level choices, introducing a new lattice method to generate all such modular invariants.

Contribution

It extends the classification of modular invariant partition functions to asymmetric (heterotic) cases and develops a generalized lattice construction method.

Findings

Identified the smallest heterotic partition functions.

Developed a generalized lattice method for constructing modular invariants.

Proved the method can generate all heterotic partition functions.

Abstract

Thus far in the search for, and classification of, `physical' modular invariant partition functions $\sum N_{LR}\,\c_L\,\C_R$ the attention has been focused on the {\it symmetric} case where the holomorphic and anti-holomorphic sectors, and hence the characters $\c_L$ and $\c_R$, are associated with the same Kac-Moody algebras $\g_L=\g_R$ and levels $k_L=k_R$. In this paper we consider the more general possibility where $(\g_L,k_L)$ may not equal $(\g_R,k_R)$. We discuss which choices of algebras and levels may correspond to well-defined conformal field theories, we find the `smallest' such {\it heterotic} (\ie asymmetric) partition functions, and we give a method, generalizing the Roberts-Terao-Warner lattice method, for explicitly constructing many other modular invariants. We conclude the paper by proving that this new lattice method will succeed in generating all the heterotic partition functions, for all choices of algebras and levels.