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arXiv · 2009.14710

Fun with $F_{24}$

Sarah M. Harrison·Natalie M. Paquette·Daniel Persson·Roberto Volpato
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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.

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Sarah M. Harrison, Natalie M. Paquette, Daniel Persson, Roberto Volpato. 2020-09-30. Fun with $F_{24}$. https://doi.org/10.1007/jhep02(2021)039

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