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Generalized kac-moody algebras from CHL dyons
, K. Gopala Krishna
Published in
Volume: 2009
Issue: 4
We provide evidence for the existence of a family of generalized Kac-Moody (GKM) superalgebras, N whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Δ(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 N-orbifolds of the heterotic string compactified on T6. 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, Δ2(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, 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. © 2009 SISSA.
About the journal
JournalJournal of High Energy Physics
Open AccessNo