The Picard-Fuchs Equations, Monodromies and Instantons in the N=2 Susy Gauge Theories

We construct the Picard-Fuchs equations of the $N=2$ supersymmetric $SU(2)$ gauge theories with $N_f=0,1,3$ matter multiplets. For the $N_f=0$ theory from the solutions of the Picard-Fuchs equation the monodromy matrices on the quantum moduli space are determined. We analyze the Seiberg-Witten solutions to compute monodromies exactly and present the instanton expansion of the periods for the $N_f=0,3$ theories.Comment: 8pages, latex, no figure

On the Monodromies of N=2 Supersymmetric Yang-Mills Theory with Gauge Group SO(2n)

We present families of algebraic curves describing the moduli-space of $N\!=\!2$ supersymmetric Yang-Mills theory with gauge group $SO(2n)$. We test our curves by computing the weak coupling monodromies and the number of $N\!=\!1$ vacua.Comment: 14 pages, 5 Postscript figures, LaTeX file, uses epsf.st

Embedding Diagrams of the N=2 Superconformal Algebra under Spectral Flow

The embedding diagrams of representations of the N=2 superconformal algebra with central charge c=3 are given. Some non-unitary representations possess subsingular vectors that are systematically described. The structure of the embedding diagrams is largely defined by the spectral flow symmetry. As an additional consistency check the action of the spectral flow on the characters is calculated.Comment: 25 pages, LaTeX, 10 figures, examples and references adde

Rotating Black Branes wrapped on Einstein Spaces

We present new rotating black brane solutions which solve Einstein's equations with cosmological constant $\Lambda$ in arbitrary dimension $d$. For negative $\Lambda$, the branes naturally appear in AdS supergravity compactifications, and should therefore play some role in the AdS/CFT correspondence. The spacetimes are warped products of a four-dimensional part and an Einstein space of dimension $d-4$, which is not necessarily of constant curvature. As a special subcase, the solutions contain the higher dimensional generalization of the Kerr-AdS metric recently found by Hawking et al.Comment: 11 pages, RevTeX, no figures, thermodynamical discussion and 2 references adde

Bi_2 Sr_2 CaCu_2 O_{8+delta} Bicrystal c-Axis Twist Josephson Junctions: A New Phase-Sensitive Test of Order Parameter Symmetry

Li {\it et al.} [Phys. Rev. Lett. {\bf 83}, 4160 (1999)] prepared atomically clean Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO) Josephson junctions between identical single crystal cleaves stacked and twisted an angle $\phi_0$ about the c axis. For each bicrystal, the ratio $J_c^J/J_c^S$ of the c-axis twist junction critical current density to that across either single crystal part is unity, independent of $\phi_0$ and the ratio $A^J/A^S$ of junction areas. From extensive theoretical studies involving a variety of tunneling and superconducting order parameter (OP) forms, we conclude that the results provide strong evidence for incoherent c-axis tunneling and that the dominant OP is s-wave for $T\le T_c$. Recently, Takano {\it et al.} [Phys. Rev. B {\bf 65}, 140315(R) (2002)] obtained results from BSCCO whisker twist junctions which also rule out a pure d-wave OP, but which are surprisingly suggestive of coherent c-axis tunneling form small Fermi surface hot spots.Comment: 5 pages, 11 figures, invited talk at LT23, to be published in Physica

Cultural transmission and optimization dynamics

We study the one-dimensional version of Axelrod's model of cultural transmission from the point of view of optimization dynamics. We show the existence of a Lyapunov potential for the dynamics. The global minimum of the potential, or optimum state, is the monocultural uniform state, which is reached for an initial diversity of the population below a critical value. Above this value, the dynamics settles in a multicultural or polarized state. These multicultural attractors are not local minima of the potential, so that any small perturbation initiates the search for the optimum state. Cultural drift is modelled by such perturbations acting at a finite rate. If the noise rate is small, the system reaches the optimum monocultural state. However, if the noise rate is above a critical value, that depends on the system size, noise sustains a polarized dynamical state.Comment: 11 pages, 10 figures include