Chiral Four-Dimensional Heterotic Covariant Lattices

TL;DR

This paper classifies right-mover lattices in chiral four-dimensional heterotic string models and analyzes the associated left-mover lattices using lattice theory, providing bounds and exploring their relation to asymmetric orbifolds.

Contribution

It provides a comprehensive classification of right-mover lattices and applies lattice genus theory to study the left-mover lattices in heterotic string vacua.

Findings

Calculated a lower bound on the number of left-mover lattices using the Smith-Minkowski-Siegel mass formula.

Established a relationship between asymmetric orbifolds and covariant lattices.

Classified all possible right-mover lattices in the context of chiral heterotic models.

Abstract

In the covariant lattice formalism, chiral four-dimensional heterotic string vacua are obtained from certain even self-dual lattices which completely decompose into a left-mover and a right-mover lattice. The main purpose of this work is to classify all right-mover lattices that can appear in such a chiral model, and to study the corresponding left-mover lattices using the theory of lattice genera. In particular, the Smith-Minkowski-Siegel mass formula is employed to calculate a lower bound on the number of left-mover lattices. Also, the known relationship between asymmetric orbifolds and covariant lattices is considered in the context of our classification.