A Comment on Fundamental Strings in M(atrix) Theory

We present a solution of M(atrix) theory describing type IIA fundamental string. Our construction is based on the central charge of the longitudinal membrane (= fundamental string), the BPS saturation condition and the relation between M(atrix) theory and supersymmetric Yang-Mills theory. The fundamental string corresponds to a photon in supersymmetric Yang-Mills theory.Comment: 11 pages + 2 uuencoded eps figures, LaTeX, errors corrected and arguments generalize

String junctions on backgrounds with a positively charged orientifold plane

By means of the heterotic/type IIB duality, we study properties of junctions on backgrounds with a positively charged orientifold seven-plane and D-branes, which are expected to give seven dimensional Sp(r) gauge theories. We give a modified BPS condition for the junctions and show that it reproduces the adjoint representation of the Sp(r) group.Comment: 16 pages + 3 eps figures, LaTeX, a reference adde

Elliptic Ding-Iohara Algebra and the Free Field Realization of the Elliptic Macdonald Operator

The Ding-Iohara algebra is a quantum algebra arising from the free field realization of the Macdonald operator. Starting from the elliptic kernel function introduced by Komori, Noumi and Shiraishi, we can define an elliptic analog of the Ding-Iohara algebra. The free field realization of the elliptic Macdonald operator is also constructed.Comment: 42 page

Right-handed Neutrinos as Superheavy Dark Matter

We propose that right-handed neutrinos are very long-lived dark matter. The long lifetime is realized by the separation of the wavefunction of right-handed neutrinos and that of other fermions in an extra dimension. Such long-lived and superheavy dark matter can naturally explain observed ultra high energy cosmic rays above the GZK cutoff (5 * 10^{19} eV) and huge amounts of cold dark matter simultaneously. Furthermore, the exponentially suppressed Yukawa couplings of right-handed neutrinos leads to the high predictablilty on the mass parameter of the neutrinoless double beta decay, as all the models which predict very small neutrino mass of one generation.Comment: 11 pages, 5 figures, to appear in JHE