How do black holes predict the sign of the Fourier coefficients of siegel modular forms?

Author： Sen Ashoke  

Publisher： Springer Publishing Company

ISSN： 0001-7701

Source： General Relativity and Gravitation, Vol.43, Iss.8, 2011-08, pp. : 2171-2183

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Abstract

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 $${Sp(2,{mathbb{Z}})}$$ 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 $${{mathbb{Z}}_N}$$ CHL models for N = 2, 3, 5, 7.

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