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Conjectured Z2-Orbifold Constructions of Self-Dual Conformal Field Theories at Central Charge 24 – the Neighborhood Graph

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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.

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  1. Department of Mathematics, University of Adelaide, Adelaide, South Australia, 5005, Australia

    P.S. Montague

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  1. P.S. Montague
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Montague, P. Conjectured Z2-Orbifold Constructions of Self-Dual Conformal Field Theories at Central Charge 24 – the Neighborhood Graph. Letters in Mathematical Physics 44, 105–120 (1998). https://doi.org/10.1023/A:1007412212350

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