Third and higher order NFPA twisted constructions of conformal field theories from lattices Original Research Article

We investigate orbifold constructions of conformal field theories from lattices by no-fixed-point automorphisms (NFPAs) Zp 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.