Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page

Static and dynamic structure factors with account of the ion structure for high-temperature alkali and alkaline earth plasmas

The electron-electron, electron-ion, ion-ion and charge-charge static structure factors are calculated for alkali (at T = 30 000 K, 60 000 K, n (e) = 0.7 x 10(21) A center dot 1.1 x 10(22) cm(-3)) and Be2+ (at T = 20 eV, n (e) = 2.5 x 10(23) cm(-3)) plasmas using the method described by Gregori et al. The dynamic structure factors for alkali plasmas are calculated at T = 30 000 K, n (e) = 1.74 x 10(20), 1.11 x 10(22) cm(-3) using the method of moments developed by Adamjan et al. In both methods the screened Hellmann-Gurskii-Krasko potential, obtained on the basis of Bogolyubov's method, has been used taking into account not only the quantum-mechanical effects but also the repulsion due to the Pauli exclusion principle. The repulsive part of the Hellmann-Gurskii-Krasko (HGK) potential reflects important features of the ion structure. Our results on the static structure factors for Be2+ plasma deviate from the data obtained by Gregori et al., while our dynamic structure factors are in a reasonable agreement with those of Adamyan et al.: at higher values of k and with increasing k the curves damp down while at lower values of k, and especially at higher electron coupling, we observe sharp peaks also reported in the mentioned work. For lower electron coupling the dynamic structure factors of Li+, Na+, K+, Rb+ and Cs+ do not differ while at higher electron coupling these curves split. As the number of shell electrons increases from Li+ to Cs+ the curves shift in the direction of low absolute value of omega and their heights diminish. We conclude that the short range forces, which we take into account by means of the HGK model potential, which deviates from the Coulomb and Deutsch ones, influence the static and dynamic structure factors significantly.The work has been realised at the Humboldt University at Berlin (Germany). One of the authors (S. P. Sadykova) would like to express sincere thanks to the Erasmus Mundus Program of the EU for the financial support and especially to Mr. M. Parske for his aid, to the Institute of Physics, Humboldt University at Berlin, for the support which made her participation at some scientific Conferences possible; I. M. T. acknowledges the financial support of the Spanish Ministerio de Educacion y Ciencia Project No. ENE2007-67406-C02-02/FTN and valuable discussions with Dr. D. Gericke.Sadykova, SP.; Ebeling, W.; Tkachenko Gorski, IM. (2011). Static and dynamic structure factors with account of the ion structure for high-temperature alkali and alkaline earth plasmas. 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