Generalized mirror symmetry and trace anomalies

We consider compactification of M-theory on X7 with betti numbers (b_0, b_1, b_2, b_3, b_3, b_2, b_1, b_0) and define a generalized mirror symmetry (b_0, b_1, b_2, b_3) goes to (b_0, b_1, b_2 -rho/2, b_3+rho/2)$ under which rho = 7b_0-5b_1+3b_2 -b_3 changes sign. Generalized self-mirror theories with rho=0 have massless sectors with vanishing trace anomaly (before dualization). Examples include pure supergravity with N \geq 4 and supergravity plus matter with N \leq 4.Comment: 19 pages late

Spanning tree generating functions and Mahler measures

We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form expressions for the spanning tree constants for all such lattices, which were previously largely unknown in all but one three-dimensional case. We show for all lattices that these can also be represented as Dirichlet $L$-series. Making the connection between spanning tree generating functions and lattice Green functions produces integral identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday. This version has additional references, additional calculations, and minor correction

Equilibration in long-range quantum spin systems from a BBGKY perspective

The time evolution of $\ell$-spin reduced density operators is studied for a class of Heisenberg-type quantum spin models with long-range interactions. In the framework of the quantum Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy, we introduce an unconventional representation, different from the usual cluster expansion, which casts the hierarchy into the form of a second-order recursion. This structure suggests a scaling of the expansion coefficients and the corresponding time scales in powers of $N^{1/2}$ with the system size $N$, implying a separation of time scales in the large system limit. For special parameter values and initial conditions, we can show analytically that closing the BBGKY hierarchy by neglecting $\ell$-spin correlations does never lead to equilibration, but gives rise to quasi-periodic time evolution with at most $\ell/2$ independent frequencies. Moreover, for the same special parameter values and in the large-$N$ limit, we solve the complete recursion relation (the full BBGKY hierarchy), observing a superexponential decay to equilibrium in rescaled time $\tau=tN^{-1/2}$.Comment: 3 figure

On the Moyal deformation of Nahm Equations in seven dimensions

We show how the reduced (anti-)self-dual Yang-Mills equations in seven dimensions described by the Nahm equations can be carried over to the Weyl-Wigner-Moyal formalism. In the process some new solutions for the cases of gauge groups SU(2) and SL(2,R) are explicitly obtained.Comment: 16+1 pages, LaTeX, no figure

Description and evaluation of the Acoustic Profiling of Ocean Currents (APOC) system used on R. V. Oceanus cruise 96 on 11-22 May 1981

The underway current profiling system which consists of a microprocessor controlled data logger that collects and formats data from a four beam Ametek-Straza 300 kHz acoustic Doppler current profiler, heading from the ship's gyrocompass, and navigation information from a Loran-C receiver and a satellite navigation unit is discussed. Data are recorded on magnetic tape and real time is calculated. Time averaging is required to remove effects of ship motion. An intercomparison is made with a moored vector measuring current meter (VMCM). The mean difference in hourly averaged APOC and VMCM currents over the four hour intercomparison is a few mm s minus including: two Gulf Stream crossings, a warm core ring survey, and shallow water in a frontal zone to the east of Nantucket Shoals

A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy

Starting from the superconformal algebras associated with $G_2$ manifolds, I extend the algebra to the manifolds with spin(7) holonomy. I show how the mirror symmetry in manifolds with spin(7) holonomy arises as the automorphism in the extended sperconformal algebra. The automorphism is realized as 14 kinds of T-dualities on the supersymmetric $T^4$ toroidal fibrations. One class of Joyce's orbifolds are pairwise identified under the symmetry.Comment: 12 pages, harvmac bi

Primordial Magnetic Fields, Right Electrons, and the Abelian Anomaly

In the standard model there are charges with abelian anomaly only (e.g. right-handed electron number) which are effectively conserved in the early universe until some time shortly before the electroweak scale. A state at finite chemical potential of such a charge, possibly arising due to asymmetries produced at the GUT scale, is unstable to the generation of hypercharge magnetic field. Quite large magnetic fields ($\sim 10^{22}$ gauss at $T\sim 100$ GeV with typical inhomogeneity scale $\sim \frac{ 10^6}{T}$) can be generated. These fields may be of cosmological interest, potentially acting as seeds for amplification to larger scale magnetic fields through non-linear mechanisms. Previously derived bounds on exotic $B-L$ violating operators may also be evaded.Comment: Revised version, to appear in Phys. Rev. Lett.. Analysis has been extended to larger chemical potentials, for which large magnetic fields survive at the electroweak scale. Previous bounds on $B-L$ violating operators are also evaded in this cas

Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field,

The finite-size scaling function of the magnetization of the ferromagnetic Heisenberg chain is argued to be universal with respect to the magnitude of the spin. The finite-size scaling function is given explicitly by an analytical calculation in the classical limit $S=\infty.$ The universality is checked for $S=1/2$ and $1$ by means of numerical calculations. Critical exponents are obtained as well. It is concluded that this universal scaling function originates in the universal behavior of the correlation function.Comment: 14 pages (revtex 2.0) + 8 PS figures upon request