Black Hole Entropy Associated with Supersymmetric Sigma Model

By means of an identity that equates elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $S^N X$ of $X$ ($S^N X=X^N/S_N$, $S_N$ is the symmetric group of $N$ elements) to the partition function of a second quantized string theory, we derive the asymptotic expansion of the partition function as well as the asymptotic for the degeneracy of spectrum in string theory. The asymptotic expansion for the state counting reproduces the logarithmic correction to the black hole entropy.Comment: 11 pages, no figures, version to appear in the Phys. Rev. D (2003

The Scientific Foundations of Forecasting Magnetospheric Space Weather

The magnetosphere is the lens through which solar space weather phenomena are focused and directed towards the Earth. In particular, the non-linear interaction of the solar wind with the Earth's magnetic field leads to the formation of highly inhomogenous electrical currents in the ionosphere which can ultimately result in damage to and problems with the operation of power distribution networks. Since electric power is the fundamental cornerstone of modern life, the interruption of power is the primary pathway by which space weather has impact on human activity and technology. Consequently, in the context of space weather, it is the ability to predict geomagnetic activity that is of key importance. This is usually stated in terms of geomagnetic storms, but we argue that in fact it is the substorm phenomenon which contains the crucial physics, and therefore prediction of substorm occurrence, severity and duration, either within the context of a longer-lasting geomagnetic storm, but potentially also as an isolated event, is of critical importance. Here we review the physics of the magnetosphere in the frame of space weather forecasting, focusing on recent results, current understanding, and an assessment of probable future developments.Peer reviewe

A measurement of the Higgs boson mass in the diphoton decay channel

A measurement of the mass of the Higgs boson in the diphoton decay channel is presented. This analysis is based on 35.9fb$^{-1}$ of proton-proton collision data collected during the 2016 LHC running period, with the CMS detector at a centre-of-mass energy of 13TeV. A refined detector calibration and new analysis techniques have been used to improve the precision of this measurement. The Higgs boson mass is measured to be m$_{H}$=125.78 ±0.26 GeV. This is combined with a measurement of mHalready performed in the H→ZZ→4${l}$ decay channel using the same data set, giving m$_{H}$=125.46 ±0.16 GeV. This result, when further combined with an earlier measurement of mHusing data collected in 2011 and 2012 with the CMS detector, gives a value for the Higgs boson mass of m$_{H}$=125.38 ±0.14 GeV. This is currently the most precise measurement of the mass of the Higgs boson