Third and Higher Order NFPA Twisted Constructions of Conformal Field Theories from Lattices

TL;DR

This paper explores orbifold constructions of conformal field theories from lattices using no-fixed-point automorphisms, focusing on the case p=3, and relates these to lattice constructions from codes, extending previous work on p=2.

Contribution

It provides explicit vertex operator expressions and analyzes locality conditions for conformal field theories derived from lattice orbifolds with NFPA automorphisms, especially for p=3.

Findings

Explicit vertex operator expressions for p=3 case.

Conditions for locality in lattice orbifold CFTs.

Connection between lattice constructions and code theory.

Abstract

We investigate orbifold constructions of conformal field theories from lattices by no-fixed-point automorphisms (NFPA's) $Z_p$ for $p$ prime, $p>2$, concentrating on the case $p=3$. Explicit expressions are given for most of the relevant vertex operators, and we consider the locality relations necessary for these to define a consistent conformal field theory. A relation to constructions of lattices from codes, analogous to that found in earlier work in the $p=2$ case which led to a generalisation of the triality structure of the Monster module, is also demonstrated.