How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?

Details How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms? How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?

2010-08-25

arxiv.org/abs/1008.4209v1

Gen.Rel.Grav.43:2171-2183,2011

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX file, 17 pages, 1 figure

Scientific paper

10.1007/s10714-011-1175-9

Single centered supersymmetric black holes in four dimensions have spherically symmetric horizon and hence carry zero angular momentum. This leads to a specific sign of the helicity trace index associated with these black holes. Since the latter are given by the Fourier expansion coefficients of appropriate meromorphic modular forms of Sp(2,Z) or its subgroup, we are led to a specific prediction for the signs of a subset of these Fourier coefficients which represent contributions from single centered black holes only. We explicitly test these predictions for the modular forms which compute the index of quarter BPS black holes in heterotic string theory on T^6, as well as in Z_N CHL models for N=2,3,5,7.

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