We study the degeneracy of quarter BPS dyons in N=4 type II compactifications of string theory. We find that the genus-two Siegel modular forms generating the degeneracies of the quarter BPS dyons in the type II theories can be expressed in terms of the genus-two Siegel modular forms generating the degeneracies of quarter BPS dyons in the CHL theories and the heterotic string. This helps us in understanding the algebra structure underlying the degeneracy of the quarter BPS states. The Conway group, Co 0, plays a role similar to Mathieu group, M 24, in the CHL models with eta quotients appearing in the place of eta products. We construct BKM Lie superalgebra structures for the ZN (for N=2, 3, 4) orbifolds of the type II string compactified on a six-torus. © 2012 Elsevier B.V.

Suresh Govindarajan

Department Of Physics

Dileep P. Jatkar

K. Gopala Krishna

Fulltext

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IIT Madras

Nuclear Physics B

Following Sen, we study the counting of ('twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with N = 4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, are given in terms of multiplicative eta products with the Mathieu group, M24, playing an important role. These multiplicative eta products enable us to construct Siegel modular forms that count twisted quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a special class of Siegel modular forms, the dd-modular forms, that have been classified by Clery and Gritsenko. We show that each one of these dd-modular forms arise as the Weyl-Kac- Borcherds denominator formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the Weyl chamber are in one-to-one correspondence with the walls of marginal stability in the corresponding CHL model for twisted dyons as well as untwisted ones. This leads to a periodic table of BKM Lie superalgebras with properties that are consistent with physical expectations. © SISSA 2011.

Journal of High Energy Physics

BKM Lie superalgebras from counting twisted CHL dyons

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.

Generalized kac-moody algebras from CHL dyons

Genus two surface and quarter BPS dyons: the contour prescription

Communications in Number Theory and Physics

Borcherds–Kac–Moody symmetry of $CN=4$ dyons

General Relativity and Gravitation

Black hole entropy function, attractors and precision counting of microstates

BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications

Journal	Nuclear Physics B
ISSN	05503213
Open Access	No