Niemeier self-dual lattices and topological phase transitions

TL;DR

This paper explores topological phase transitions in 2D sigma-models linked to Niemeier lattices, revealing how lattice properties influence critical behavior and discussing potential applications in string theory.

Contribution

It introduces a novel connection between Niemeier lattices and topological phase transitions, highlighting the role of Coxeter numbers in critical properties.

Findings

Critical properties are determined by Coxeter numbers of lattices

Analysis of integer-valued lattices with minimal norm 1 or 2

Discussion of applications to string theory

Abstract

A topological phase transition in two-dimensional nonlinear sigma-models on tori, connected with self-dual (unimodular) 24-dimensional Niemeier lattices, is considered. It is shown that critical properties of these transitions are determined by corresponding Coxeter numbers of lattices. A case of general integer-valued lattices with minimal norm equal 1 or 2 and a possible application to string theory are discussed.