Niemeier Lattices in the Free Fermionic Heterotic-String Formulation

TL;DR

This paper explores the connection between Niemeier lattices, heterotic-string compactifications, and moonshine symmetries using free fermionic methods, aiming to classify symmetries in two-dimensional heterotic-string theories.

Contribution

It introduces a novel classification approach for two-dimensional heterotic-string symmetries using Niemeier lattices and free fermionic techniques, linking string dualities and moonshine symmetries.

Findings

Classification of symmetries in 2D heterotic-string theories.

Identification of Niemeier lattices relevant to string compactifications.

Insights into the structure of heterotic-string dualities.

Abstract

The spinor-vector duality was discovered in free fermionic constructions of the heterotic-string in four dimensions. It played a key role in the construction of heterotic-string models with an anomaly free extra $Z^\prime$ symmetry that may remain unbroken down to low energy scales. A generic signature of the low scale string derived $Z^\prime$ model is via di-photon excess that may be within reach of the LHC. A fascinating possibility is that the spinor-vector duality symmetry is rooted in the structure of the heterotic-string compactifications to two dimensions. The two dimensional heterotic-string theories are in turn related to the so-called moonshine symmetries that underlie the two dimensional compactifications. In this paper we embark on exploration of this connection by the free fermionic formulation to classify the symmetries of the two dimensional heterotic-string theories. We use two complementary approaches in our classification. The first utilises a construction which is akin to the one used in the spinor-vector duality. Underlying this method is the triality property of $SO(8)$ representations. In the second approach we use the free fermionic tools to classify the twenty four dimensional Niemeier lattices.