Conjectured Z_2-Orbifold Constructions of Self-Dual Conformal Field Theories at Central Charge 24 - the Neighborhood Graph

Details Conjectured Z_2-Orbifold Constructions of Self-Dual Conformal Field Theories at Central Charge 24 - the Neighborhood Graph Conjectured Z_2-Orbifold Constructions of Self-Dual Conformal Field Theories at Central Charge 24 - the Neighborhood Graph

1997-09-11

arxiv.org/abs/hep-th/9709076v1

Lett.Math.Phys. 44 (1998) 105-120

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, LaTeX

Scientific paper

By considering constraints on the dimensions of the Lie algebra corresponding to the weight one states of Z_2 and Z_3 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 Z_2 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.

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