Generalized Kac-Moody Algebras from CHL dyons

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dc.creatorGovindarajan, Suresh
dc.creatorKrishna, K Gopala
dc.date2008-07-28
dc.date2009-03-17
dc.date.accessioned2026-07-07T13:04:37Z
dc.date.available2026-07-07T13:04:37Z
dc.descriptionWe 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.
dc.descriptionLaTeX, 35 pages; v2: improved referencing and discussion; typos corrected; v3 [substantial revision] 44 pages, modularity of additive lift proved, product representation of the forms also given; further references added
dc.identifierhttps://arxiv.org/abs/0807.4451
dc.identifierhttp://arxiv.org/abs/0807.4451
dc.identifierJHEP 0904:032,2009
dc.identifierdoi:10.1088/1126-6708/2009/04/032
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227229
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.titleGeneralized Kac-Moody Algebras from CHL dyons
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