Conjectured Z 2 -Orbifold Constructions of Self-Dual Conformal Field Theories at Central Charge 24 – the Neighborhood Graph

Abstract

By considering constraints on the dimensions of the Lie algebra corresponding to the weight 1-states of Z2 and Z3 orbifold models arising from imposing the appropriate modular properties on the graded characters of the automorphisms on the underlying conformal field theory, we propose a set of constructions of all but one of the 71 self-dual meromorphic bosonic conformal field theories at central charge 24. In the Z2 case, this leads to an extension of the neighborhood graph of the even self-dual lattices in 24 dimensions to conformal field theories, and we demonstrate that the graph becomes disconnected.