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

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.Comment: LaTeX file, 17 pages, 1 figur

A new species of Archaeoryctes from the Middle Paleocene of China and the phylogenetic diversification of Didymoconidae

Didymoconidae are an enigmatic group of Asian endemic insectivorous mammals. We describe the new didymoconid species Archaeoryctes wangi sp. nov. from the Upper Member of the Wanghudun Formation (Middle Paleocene). This new species from the Qianshan Basin (Anhui Province, China) forms an interesting geographical intermediate between A. notialis from South China and A. borealis and A. euryalis from the Mongolian Plateau. To better understand the origin and evolutionary diversification of Didymoconidae, we performed a cladistic and stratocladistic study of the Didymoconidae and various outgroups. This study of dental material did not resolve the higher level affinities of Didymoconidae, but confirms the validity of the family and its distinctiveness from the morphologically similar Sarcodontidae. Moreover, our results corroborate the current didymoconid classification with the distinction of three subfamilies: “Ardynictinae”, Kennatheriinae and Didymoconinae; “Ardynictinae” are a paraphyletic stemgroup for the two other subfamilies. Our results suggest three distinct didymoconid radiations: (1) primitive ardynictines appeared in South China from the start of the Nongshanian; their evolution continues on the Mongolian Plateau with (2) the radiation of more evolved ardynictines and kennatheriines at the start of the Middle Eocene Arshantan and (3) the origin of didymoconines at the start of the Late Eocene Ergilian

Three String Junction and N=4 Dyon Spectrum

The exact spectrum of dyons in a class of N=4 supersymmetric string theories gives us information about dyon spectrum in N=4 supersymmetric gauge theories. This in turn can be translated into prediction about the BPS spectrum of three string junctions on a configuration of three parallel D3-branes. We show that this prediction agrees with the known spectrum of three string junction in different domains in the moduli space separated by walls of marginal stability.Comment: LaTeX file, 14 page