F^4 Terms in N=4 String Vacua

We discuss $F_{\mu\nu}^4$ terms in torroidal compactifications of type-I and heterotic SO(32) string theory. We give a simple argument why only short BPS multiplets contribute to these terms at one loop, and verify heterotic-type-I duality to this order.Comment: 10 pages, Latex. A statement about superinvariants was corrected. Minor cosmetic changes were also made. To appear in Proceedings of Trieste Spring School and Workshop, April 199

An Initial Value Problem for Oscillations of the Interstellar Gas

Initial value problem for oscillations in interstellar ga

On the classification of (2,1) heterotic strings

We classify all untwisted (2,1) heterotic strings. The only solutions are the three already known cases, having massless spectra consisting either of 24 chiral fermions, or of 24 bosons, or of 8 scalars and 8 fermions of each chirality.Comment: Phyzzx and Tables macro packages require

On Heterotic/Type I Duality in d=8

We discuss heterotic corrections to quartic internal U(1) gauge couplings and check duality by calculating one-loop open string diagrams and identifying the D-instanton sum in the dual type I picture. We also compute SO(8)^4 threshold corrections and finally R^2 corrections in type I theory.Comment: 9 pages, Latex, To appear in the proceedings of "Quantum Aspects of Gauge Theories, Supersymmetries and Unification", Corfu, September 199

Chiral Rings, Vacua and Gaugino Condensation of Supersymmetric Gauge Theories

We find the complete chiral ring relations of the supersymmetric U(N) gauge theories with matter in adjoint representation. We demonstrate exact correspondence between the solutions of the chiral ring and the supersymmetric vacua of the gauge theory. The chiral ring determines the expectation values of chiral operators and the low energy gauge group. All the vacua have nonzero gaugino condensation. We study the chiral ring relations obeyed by the gaugino condensate. These relations are generalizations of the formula $S^N=\Lambda^{3N}$ of the pure ${\cal N} =1$ gauge theory.Comment: 38 page

Free-field Representations and Geometry of some Gepner models

The geometry of $k^{K}$ Gepner model, where $k+2=2K$ is investigated by free-field representation known as "bc\bet\gm"-system. Using this representation it is shown directly that internal sector of the model is given by Landau-Ginzburg $\mathbb{C}^{K}/\mathbb{Z}_{2K}$-orbifold. Then we consider the deformation of the orbifold by marginal anti-chiral-chiral operator. Analyzing the holomorphic sector of the deformed space of states we show that it has chiral de Rham complex structure of some toric manifold, where toric dates are given by certain fermionic screening currents. It allows to relate the Gepner model deformed by the marginal operator to the $\sigma$-model on CY manifold realized as double cover of $\mathbb{P}^{K-1}$ with ramification along certain submanifold.Comment: LaTex, 14 pages, some acknowledgments adde

Generalized Calabi-Yau Manifolds and the Mirror of a Rigid Manifold

We describe the mirror of the Z orbifold as a representation of a class of generalized Calabi-Yau manifolds that can be realized as manifolds of dimension five and seven. Despite their dimension these correspond to superconformal theories with $c=9$ and so are perfectly good for compactifying the heterotic string to the four dimensions of space-time. As a check of mirror symmetry we compute the structure of the space of complex structures of the mirror and check that this reproduces the known results for the Yukawa couplings and metric appropriate to the Kahler class parameters on the Z orbifold together with their instanton corrections.Comment: 39 pages, plain Te

Estimating the size of the cosmic-ray halo using particle distribution moments

Context: Particle transport in many astrophysical problems can be described either by the Fokker–Planck equation or by an equivalent system of stochastic differential equations. Aims: It is shown that the latter method can be applied to the problem of defining the size of the cosmic-ray galactic halo. Methods: Analytical expressions for the leading moments of the pitch-angle distribution of relativistic particles are determined. Particle scattering and escape are analyzed in terms of the moments. Results: In the case of an anisotropic distribution, the first moment leads to an expression for the halo size, identified with the particle escape from the region of strong scattering. Previous studies are generalized by analyzing the case of a strictly isotropic initial distribution. A new expression for the variance of the distribution is derived, which illustrates the anisotropization of the distribution. Conclusions: Stochastic calculus tools allow one to analyze physically motivated forms for the scattering rate, so that a detailed realistic model can be developed