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

More on complexity of operators in quantum field theory

Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous systems. By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten $p$-norm type. We also clarify the relation between our complexity and other works. First, we show that our results in a bi-invariant geometry are consistent with the ones in a right-invariant geometry such as $k$-local geometry. Here, a careful analysis of the sectional curvature is crucial. Second, we show that our complexity can concretely realize the conjectured pattern of the time-evolution of the complexity: the linear growth up to saturation time. The saturation time can be estimated by the relation between the topology and curvature of SU($n$) groups.Comment: Modified the Sec. 4.1, where we offered a powerful proof: if (1) the ket vector and bra vector in quantum mechanics contain same physics, or (2) adding divergent terms to a Lagrangian will not change underlying physics, then complexity in quantum mechanics must be bi-invariant