Fun with F24
Journal article, 2021

We study some special features of F24, 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 F24, 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 F24, with the admissible choices labeled by the semisimple Lie algebras of dimension 24. We also discuss how F24, 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 E8 lattice.

Conformal Field Theory

BRST Quantization

Conformal and W Symmetry

Conformal Field Models in String Theory


Sarah M. Harrison

McGill University

N. M. Paquette

Institute for Advanced Studies

California Institute of Technology (Caltech)

Daniel Persson

University of Gothenburg

Chalmers, Mathematical Sciences, Algebra and geometry

R. Volpato

University of Padua

Journal of High Energy Physics

1126-6708 (ISSN) 1029-8479 (eISSN)

Vol. 2021 2 39

Subject Categories

Algebra and Logic


Mathematical Analysis



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Latest update

5/5/2021 1