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

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.

LaTeX 46 pages

References in corpus (5)

• Meromorphic c=24 Conformal Field Theories
• Conformal Field Theories, Representations and Lattice Constructions
• Orbifold Constructions and the Classification of Self-Dual c=24 Conformal Field Theories
• Classification of Ten-Dimensional Heterotic Strings
• Seventy Relatives of the Monster Module

Cited by in corpus (6)

• Orbifold Constructions and the Classification of Self-Dual c=24 Conformal Field Theories
• 51 constructions of the Moonshine module
• A Self-Dual Integral Form of the Moonshine Module
• On Zhu's Associative Algebra as a Tool in the Representation Theory of Vertex Operator Algebras
• On the Uniqueness of the Twisted Representation in the Z_2 Orbifold Construction of a Conformal Field Theory from a Lattice
• Intertwiners in Orbifold Conformal Field Theories