Generalized Kac-Moody Algebras from CHL dyons

TL;DR

This paper constructs and analyzes a family of generalized Kac-Moody superalgebras linked to CHL dyons, revealing their automorphic forms and potential role in BPS state algebra in string theory.

Contribution

It introduces new GKM superalgebras associated with CHL dyons and connects their automorphic forms to genus-two modular forms, expanding the understanding of algebraic structures in string compactifications.

Findings

Existence of GKM superalgebras G_N with specific modular form denominator formulas.

Automorphic forms are additive lifts of Jacobi forms of certain weights and indices.

Orbifolding affects the imaginary roots of the superalgebras, leaving real roots unchanged.

Abstract

We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6), (3,4), and possibly (5,2). The square of the automorphic form is the modular transform of the generating function of the degeneracy of CHL dyons in asymmetric Z_N-orbifolds of the heterotic string compactified on T^6. The new generalized Kac-Moody superalgebras all arise as different `automorphic corrections' of the same Lie algebra and are closely related to a generalized Kac-Moody superalgebra constructed by Gritsenko and Nikulin. The automorphic forms, Delta_{k/2}(Z), arise as additive lifts of Jacobi forms of (integral) weight k/2 and index 1/2. We note that the orbifolding acts on the imaginary simple roots of the unorbifolded GKM superalgebra, G_1 leaving the real simple roots untouched. We anticipate that these superalgebras will play a role in understanding the `algebra of BPS states' in CHL compactifications.