Novel Symmetry of Non-Einsteinian Gravity in Two Dimensions

The integrability of $R^2$-gravity with torsion in two dimensions is traced to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian phase space. It may be interpreted as a quadratically deformed $iso(2,1)$-algebra with the deformation consisting of the Casimir operators of the undeformed algebra. The locally conserved quantity encountered in the explicit solution is identified as an element of the centre of this algebra. Specific contractions of the algebra are related to specific limits of the explicit solutions of this model.Comment: 17 pages, TUW-92-04 (LaTeX

A Note on Marginally Stable Bound States in Type II String Theory

Spectrum of elementary string states in type II string theory contains ultra-short multiplets that are marginally stable. $U$-duality transformation converts these states into bound states at threshold of $p$-branes carrying Ramond-Ramond charges, and wrapped around $p$-cycles of a torus. We propose a test for the existence of these marginally stable bound states. Using the recent results of Polchinski and of Witten, we argue that the spectrum of bound states of $p$-branes is in agreement with the prediction of $U$-duality.Comment: LaTeX file, 6 page

Weak Scale Superstrings

Recent developments in string duality suggest that the string scale may not be irrevocably tied to the Planck scale. Two explicit but unrealistic examples are described where the ratio of the string scale to the Planck scale is arbitrarily small. Solutions which are more realistic may exist in the intermediate coupling or ``truly strong coupling'' region of the heterotic string. Weak scale superstrings have dramatic experimental consequences for both collider physics and cosmology.Comment: harvmac, 14 pages. References added, 3 typos fixed, Comments added at beginning of section 4 emphasizing flaws of the toy example

Quantum kk-core conduction on the Bethe lattice

Classical and quantum conduction on a bond-diluted Bethe lattice is considered. The bond dilution is subject to the constraint that every occupied bond must have at least $k-1$ neighboring occupied bonds, i.e. $k$-core diluted. In the classical case, we find the onset of conduction for $k=2$ is continuous, while for $k=3$, the onset of conduction is discontinuous with the geometric random first-order phase transition driving the conduction transition. In the quantum case, treating each occupied bond as a random scatterer, we find for $k=3$ that the random first-order phase transition in the geometry also drives the onset of quantum conduction giving rise to a new universality class of Anderson localization transitions.Comment: 12 pgs., 6 fig

Kaluza-Klein electrically charged black branes in M-theory

We present a class of Kaluza-Klein electrically charged black p-brane solutions of ten-dimensional, type IIA superstring theory. Uplifting to eleven dimensions these solutions are studied in the context of M-theory. They can be interpreted either as a p+1 extended object trapped around the eleventh dimension along which momentum is flowing or as a boost of the following backgrounds: the Schwarzschild black (p+1)-brane or the product of the (10-p)-dimensional Euclidean Schwarzschild manifold with the (p+1)-dimensional Minkowski spacetime.Comment: 16 pages, uses latex and epsf macro, figures include

Tycho Brahe's supernova: light from centuries past

The light curve of SN 1572 is described in the terms used nowadays to characterize SNeIa. By assembling the records of the observations done in 1572--74 and evaluating their uncertainties, it is possible to recover the light curve and the color evolution of this supernova. It is found that, within the SNe Ia family, the event should have been a SNIa with a normal rate of decline, its stretch factor being {\it s} $\sim$ 0.9. Visual light curve near maximum, late--time decline and the color evolution sustain this conclusion. After correcting for extinction, the luminosity of this supernova is found to be M$_{V}$ $=$ --19.58 --5 log (D/3.5 kpc) $\pm$ 0.42.Comment: 28 pages, 3 figures, 3 tables. submitted to ApJ (Main Journal

Duality Symmetry in the Schwarz-Sen Model

The continuous extension of the discrete duality symmetry of the Schwarz-Sen model is studied. The corresponding infinitesimal generator $Q$ turns out to be local, gauge invariant and metric independent. Furthermore, $Q$ commutes with all the conformal group generators. We also show that $Q$ is equivalent to the non---local duality transformation generator found in the Hamiltonian formulation of Maxwell theory. We next consider the Batalin--Fradkin-Vilkovisky formalism for the Maxwell theory and demonstrate that requiring a local duality transformation lead us to the Schwarz--Sen formulation. The partition functions are shown to be the same which implies the quantum equivalence of the two approaches.Comment: 10 pages, latex, small changes, final version to appear in Phys. Rev.