Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories

The $u$-plane integrals of topologically twisted $N = 2$ supersymmetric gauge theories generally contain contact terms of nonlocal topological observables. This paper proposes an interpretation of these contact terms from the point of view of integrable hierarchies and their Whitham deformations. This is inspired by Mari\~no and Moore's remark that the blowup formula of the $u$-plane integral contains a piece that can be interpreted as a single-time tau function of an integrable hierarchy. This single-time tau function can be extended to a multi-time version without spoiling the modular invariance of the blowup formula. The multi-time tau function is comprised of a Gaussian factor $e^{Q(t_1,t_2,...)}$ and a theta function. The time variables $t_n$ play the role of physical coupling constants of 2-observables $I_n(B)$ carried by the exceptional divisor $B$. The coefficients $q_{mn}$ of the Gaussian part are identified to be the contact terms of these 2-observables. This identification is further examined in the language of Whitham equations. All relevant quantities are written in the form of derivatives of the prepotential.Comment: latex, 17 pages, no figures; final version for publicatio

Anomalous increase of solar anisotropy above 150GV in 1981-1983

An analysis was carried out of the observed data with Nagoya (surface). Misato (34mwe) and Sakashita (80mwe) multidirectional muon telescope, for the solar activity maximum period of 1978-1983. These data respond to primaries extending over the median rigidity range 60GV to 600GV. The observed amplitude at Sakashita station in 1981-1983 increased, especially in 1982; the amplitude is twice as large as that in 1978-1980, when those at Nagoya and Misato stations are nearly the same as those in 1978-1980. Uni-directional anisotropy is derived by the best fit method by assuming the flat rigidity spectrum with the upper cutoff rigidity Pu. The value of Pu obtained is 270GV in 1981-1983 and 150GV in 1978-1980

Solar tri-diurnal variation of cosmic rays in a wide range of rigidity

Solar tri-diurnal variations of cosmic rays have been analyzed in a wide range of rigidity, using data from neutron monitors, and the surface and underground muon telescopes for the period 1978-1983. The rigidity spectrum of the anisotropy in space is assumed to be of power-exponential type as (P/gamma P sub o) to the gamma exp (gamma-P/P sub o). By means of the best-fit method between the observed and the expected variations, it is obtained that the spectrum has a peak at P (=gamma P sub o) approx = 90 GV, where gamma=approx 3.0 and P sub o approx. 30 GV. The phase in space of the tri-diurnal variation is also obtained as 7.0 hr (15 hr and 23 hr LT), which is quite different from that of approx. 1 hr. arising from the axisymmetric distribution of cosmic rays with respect to the IMF

Field Effect Transistor Based on KTaO3 Perovskite

An n-channel accumulation-type field effect transistor (FET) has been fabricated utilizing a KTaO3 single crystal as an active element and a sputtered amorphous Al2O3 film as a gate insulator. The device demonstrated an ON/OFF ratio of 10^4 and a field effect mobility of 0.4cm^2/Vs at room temperature, both of which are much better than those of the SrTiO3 FETs reported previously. The field effect mobility was almost temperature independent down to 200K. Our results indicate that the Al2O3 / KTaO3 interface is worthy of further investigations as an alternative system of future oxide electronics.Comment: 3 pages, 3 Postscript figures, submitted to Appl.Phys.Let

Field-Effect Transistor on SrTiO3 with sputtered Al2O3 Gate Insulator

A field-effect transistor that employs a perovskite-type SrTiO3 single crystal as the semiconducting channel is revealed to function as n-type accumulation-mode device with characteristics similar to that of organic FET's. The device was fabricated at room temperature by sputter-deposition of amorphous Al2O3 films as a gate insulator on the SrTiO3 substrate. The field-effect(FE) mobility is 0.1cm2/Vs and on-off ratio exceeds 100 at room temperature. The temperature dependence of the FE mobility down to 2K shows a thermal-activation-type behavior with an activation energy of 0.6eV

A class of integrable lattices and KP hierarchy

We introduce a class of integrable $l$-field first-order lattices together with corresponding Lax equations. These lattices may be represented as consistency condition for auxiliary linear systems defined on sequences of formal dressing operators. This construction provides simple way to build lattice Miura transformations between one-field lattice and $l$-field ($l\ge 2$) ones. We show that the lattices pertained to above class is in some sense compatible with KP flows and define the chains of constrained KP Lax operators.Comment: LaTeX, 13 pages, accepted for publication in J. Phys. A: Math. Ge

Conifold geometries, topological strings and multi-matrix models

We study open B-model representing D-branes on 2-cycles of local Calabi--Yau geometries. To this end we work out a reduction technique linking D-branes partition functions and multi-matrix models in the case of conifold geometries so that the matrix potential is related to the complex moduli of the conifold. We study the geometric engineering of the multi-matrix models and focus on two-matrix models with bilinear couplings. We show how to solve this models in an exact way, without resorting to the customary saddle point/large N approximation. The method consists of solving the quantum equations of motion and using the flow equations of the underlying integrable hierarchy to derive explicit expressions for correlators. Finally we show how to incorporate in this formalism the description of several group of D-branes wrapped around different cycles.Comment: 35 pages, 5.3 and 6 revise

Hard X-ray Luminosities of Multinuclei Infrared Luminous Galaxies Showing a Radio/Far-Infrared Excess

We report the results of hard X-ray observations of four multinuclei merging infrared luminous galaxies (IRLGs). We selected these four sources for their excess of radio to far-infrared luminosity ratio compared with starburst galaxies. This excess suggests that activity associated with a supermassive black hole (SMBH) contributes strongly to the IRLGs' bolometric luminosities. Although we expect strong hard X-ray emission from the SMBH-driven activity, the radio-excess multinuclei merging IRLGs show considerably smaller hard X-ray luminosities relative to far-infrared (40$-$500 $\mu$m) and infrared (8$-$1000 $\mu$m) luminosities than active galactic nuclei (AGNs) showing a similar radio-excess. This result may demonstrate that emission in the hard X-ray region from SMBH-driven activity in the multinuclei merging IRLGs is severely suppressed compared to a typical spectral energy distribution of SMBH-driven activity in AGNs. If this is a common property of merging IRLGs, without its correction, hard X-ray observations underestimate the contribution of SMBH-driven activity to the bolometric luminosities of merging IRLGs.Comment: 25 pages of text, 4 figures, aaspp4.sty, Astrophysical Journal, in press (1999, Volume 527

Matrix biorthogonal polynomials on the unit circle and non-Abelian Ablowitz-Ladik hierarchy

Adler and van Moerbeke \cite{AVM} described a reduction of 2D-Toda hierarchy called Toeplitz lattice. This hierarchy turns out to be equivalent to the one originally described by Ablowitz and Ladik \cite{AL} using semidiscrete zero-curvature equations. In this paper we obtain the original semidiscrete zero-curvature equations starting directly from the Toeplitz lattice and we generalize these computations to the matrix case. This generalization lead us to the semidiscrete zero-curvature equations for the non-abelian (or multicomponent) version of Ablowitz-Ladik equations \cite{GI}. In this way we extend the link between biorthogonal polynomials on the unit circle and Ablowitz-Ladik hierarchy to the matrix case.Comment: 23 pages, accepted on publication on J. Phys. A., electronic link: http://stacks.iop.org/1751-8121/42/36521