Fun with F24

Abstract

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 N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 1 supersymmetric version of the chiral CFT based on the E 8 lattice.

Keywords

• Conformal and W Symmetry
• Conformal Field Models in String Theory
• Conformal Field Theory
• BRST Quantization