Fun with $F_{24}$

Abstract

We study some special features of $F_{24}$, the holomorphic $c=12$ superconformal field theory (SCFT) given by 24 chiral free fermions. We construct eight different Lie superalgebras of "physical" states of a chiral superstring compactified on $F_{24}$, and we prove that they all have the structure of Borcherds-Kac-Moody superalgebras. This produces a family of new examples of such superalgebras. The models depend on the choice of an $\mathcal{N}=1$ supercurrent on $F_{24}$, with the admissible choices labeled by the semisimple Lie algebras of dimension 24. We also discuss how $F_{24}$, with any such choice of supercurrent, can be obtained via orbifolding from another distinguished $c=12$ holomorphic SCFT, the $\mathcal{N}=1$ supersymmetric version of the chiral CFT based on the $E_8$ lattice.

arXiv comment46 pages. v2: minor corrections

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Cited by in corpus (4)

• Topological modularity of Supermoonshine
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• BPS Algebras in 2D String Theory
• Non-invertible defects from the Conway SCFT to K3 sigma models I: general results