Heterotic Modular Invariants and Level--Rank Duality

TL;DR

This paper introduces new heterotic modular invariants derived from level-rank duality, supporting the consistency of heterotic WZW conformal field theories and comparing dual-flip with conformal subalgebra methods.

Contribution

It presents novel heterotic modular invariants based on level-rank duality and introduces the dual-flip construction, enhancing understanding of heterotic conformal field theories.

Findings

New heterotic modular invariants discovered

Complete list of certain level-one heterotic invariants obtained

Proved a conjecture on exceptional A_{r,k} invariants and duality

Abstract

New heterotic modular invariants are found using the level-rank duality of affine Kac-Moody algebras. They provide strong evidence for the consistency of an infinite list of heterotic Wess-Zumino-Witten (WZW) conformal field theories. We call the basic construction the dual-flip, since it flips chirality (exchanges left and right movers) and takes the level-rank dual. We compare the dual-flip to the method of conformal subalgebras, another way of constructing heterotic invariants. To do so, new level-one heterotic invariants are first found; the complete list of a specified subclass of these is obtained. We also prove (under a mild hypothesis) an old conjecture concerning exceptional $A_{r,k}$ invariants and level-rank duality.