Fun with F 24

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 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 𝒩 = 1 supersymmetric version of the chiral CFT based on the E 8 lattice.