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On membrane interactions and a three-dimensional analog of Riemann surfaces
Get PDFMembranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of 3 connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions
Einstein’s cosmology review of 1933: a new perspective on the Einstein-de Sitter model of the cosmos
Get PDFWe present a first English translation and analysis of a little-known review of relativistic cosmology written by Albert Einstein in late 1932. The article, which was published in 1933 in a book of Einstein papers translated into French, contains a substantial review of static and dynamic relativistic models of the cosmos, culminating in a discussion of the Einstein-de Sitter model. The article offers a valuable contemporaneous insight into Einstein’s cosmology in the early 1930s and confirms that his interest lay in the development of the simplest model of the cosmos that could account for observation, rather than an exploration of all possible cosmic models. The article also confirms that Einstein did not believe that simplistic relativistic models could give an accurate description of the early universe
Higgs- and Skyrme–Chern–Simons densities in all dimensions
Get PDFTwo types of new Chern-Simons (CS) densities, both defined in all odd and even dimensions, are proposed. These new CS densities feature a scalar field interacting with a scalar. In one case this is a Higgs scalar while in the other it is a Skyrme scalar. The motivation is to study the effects of adding these new CS terms to a Lagrangian which supports static soliton solutions prior to their introduction
Charged isotropic non-Abelian dyonic black branes
Get PDFWe construct black holes with a Ricci flat horizon in Einstein–Yang-Mills theory with a negative cosmological constant, which approach asymptotically an AdS_d spacetime background (with d ≥ 4). These solutions are isotropic, i.e. all space directions in a hypersurface of constant radial and time coordinates are equivalent, and possess both electric and magnetic fields. We find that the basic properties of the non-Abelian solutions are similar to those of the dyonic isotropic branes in Einstein-Maxwell theory (which, however, exist in even spacetime dimensions only). These black branes possess a nonzero magnetic field strength on the flat boundary metric, which leads to a divergent mass of these solutions, as defined in the usual way. However, a different picture is found for odd spacetime dimensions, where a non-Abelian Chern-Simons term can be incorporated in the action. This allows for black brane solutions with a magnetic field which vanishes asymptotically
Amplitude and recurrence time analysis of LP activity at Mount Etna, Italy
Get PDFThe aim of this work is to improve our understanding of the long-period (LP) source mechanism at Mount Etna (Italy) through a statistical analysis of detailed LP catalogues. The behavior of LP activity is compared with the empirical laws governing earthquake recurrence, in order to investigate whether any relationships exist between these two apparently different earthquake classes. We analyzed a family of 8894 events detected during a temporary experiment in August 2005. For that time interval, the LP activity is
sustained in time and the volcano did not exhibit any evident sign of unrest. The completeness threshold of the catalogue is established through a detection test based on synthetic waveforms. The retrieved amplitude distribution differs significantly from the Gutenberg-Richter law, and the interevent times distribution does not follow the typical γ law, expected for tectonic activity. In order to compare these results with a catalogue for which the source mechanism is well established, we applied the same procedure to a data set from Stromboli Volcano, where recurrent LP activity is closely related to very-long-period pulses, in turn associated with the summit explosions. Our results indicate that the two catalogues exhibit similar behavior in terms of amplitude and interevent time distributions. This suggests that the Etna’s LP signals are most likely driven
by stress changes caused by an intermittent degassing process occurring at depth, similar to that which drives the summit explosions at Stromboli Volcano
Commuting Quantum Matrix Models
Get PDFWe study a quantum system of p commuting matrices and find that such a quantum system requires an explicit curvature dependent potential in its Lagrangian for the system to have a finite energy ground state. In contrast it is possible to avoid such curvature dependence in the Hamiltonian. We study the eigenvalue distribution for such systems in the large matrix size limit. A critical rôle is played by p = 4. For p ≥ 4 the competition between eigenvalue repulsion and the attractive potential forces the eigenvalues to form a sharp spherical shell
Holographic Bilayer/Monolayer Phase Transitions
Get PDFIn the present work, we discuss the phase structure of bilayer and monolayer phases in the (2+1)-dimensional defect field theory whose gravity dual is obtained by embedding D5/anti-D5 probe flavour branes in the singular conifold. We study in detail the embedding equations and compare the free energies of the resulting configurations at non-zero temperature and external magnetic field perpendicular to the defects. Moreover, we analyse the meson spectrum and confirm the stability of the single bilayer solution
Persistent Shallow Background Microseismicity on Hekla Volcano, Iceland: A Potential Monitoring Tool
Get PDFHekla is one of Iceland's most active volcanoes. Since 1970 it has erupted four times with a period of quiescence of 14 years since the last eruption. We detected persistent levels of background microseismicity with a temporary seismic network in autumn 2012. An amplitude based as well as an arrival-time based location method was applied to two populations of events and located them at shallow depths on the northern flank, close to the summit. This seismicity has not been identified previously by the permanent seismic network in Iceland as it is below its detection threshold. The detected events were either short, higher frequency events with distinct arrivals located beneath the summit on the northern flank of Hekla or longer, emergent, lower frequency events about 4 km northeast of the summit at 200–400 m depth below the surface. Estimated moment magnitudes were MW = -1.1 to -0.1 and MW = -0.9 to -0.0 and local magnitudes ML = -0.5 to +0.3 and ML = -0.3 to +0.3, respectively. This seismicity does not show any correlation with gas output but is located at the steepest slopes of the edifice. Hence we suggest that the current shallow microseismicity at Hekla is structurally controlled. This offers a possible opportunity of using near summit microseismicity as a tool for monitoring emerging unrest at Hekla. Microseismicity rates will be very sensitive to small stress perturbations due to magma migration at depth. Currently in the absence of microseismicity monitoring, Hekla switches from apparently quiescent to fully eruptive on the order of only 1 h