Transformations among large c conformal field theories

TL;DR

This paper explores transformations linking all 24-dimensional Niemeier lattices and extends these ideas to higher-dimensional conformal field theories, revealing periodicities in their partition functions and connections to the Monster group.

Contribution

It introduces a set of transformations connecting Niemeier lattices and constructs higher-dimensional CFTs with spectra related to the Monster group.

Findings

Transformations relate all Niemeier lattices.

Construction of c=24k theories with Monster symmetry.

Periodicities observed in extremal partition functions.

Abstract

We show that there is a set of transformations that relates all of the 24 dimensional even self-dual (Niemeier) lattices, and also leads to non-lattice objects that however cannot be interpreted as a basis for the construction of holomorphic conformal field theory. In the second part of this paper, we extend our observations to higher dimensional conformal field theories build on extremal partition functions, where we generate c=24k theories with spectra decomposable into the irreducible representations of the Fischer-Griess Monster. We observe interesting periodicities in the coefficients of extremal partition functions and characters of the extremal vertex operator algebras.