Abstract
A recently discovered relation between 4D and 5D black holes is used to derive weighted BPS black hole degeneracies for 4D N=4 string theory from the well-known 5D degeneracies. They are found to be given by the Fourier coefficients of the unique weight 10 automorphic form of the modular group Sp(2,Z). This result agrees exactly with a conjecture made some years ago by Dijkgraaf, Verlinde and Verlinde.
Highlights
A general D0-D2-D4-D6 black hole in a 4D IIA string compactification has an M-theory lift to a 5D black hole configuration in a multi-Taub-NUT geometry
N = 4 string theory in four dimensions can be obtained from IIA compactification on K3 × T 2
And elsewhere in this paper by “degeneracies,” in a slight abuse of language, we mean the number of bosons minus the number of fermions of a given charge, and the center-ofmass multiplet is factored out. These microscopic BPS degeneracies d5 of the D1-D5 system are well known [2, 3]. Their main contribution comes from the coefficients in the Fourier expansion of the elliptic genus of HilbN (K3): χN (ρ, ν) =
Summary
Strominger, Andrew, David Shih, and Xi Yin. 2006. “Recounting Dyons in N = 4 String Theory.” Journal of High Energy Physics 2006 (10): 087–087. https://doi.org/10.1088/1126-6708/2006/10/087. This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-ofuse#LAA
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