Dynamical Formation of Horizons in Recoiling D Branes

A toy calculation of string/D-particle interactions within a world-sheet approach indicates that quantum recoil effects - reflecting the gravitational back-reaction on space-time foam due to the propagation of energetic particles - induces the appearance of a microscopic event horizon, or `bubble', inside which stable matter can exist. The scattering event causes this horizon to expand, but we expect quantum effects to cause it to contract again, in a `bounce' solution. Within such `bubbles', massless matter propagates with an effective velocity that is less than the velocity of light in vacuo, which may lead to observable violations of Lorentz symmetry that may be tested experimentally. The conformal invariance conditions in the interior geometry of the bubbles select preferentially three for the number of the spatial dimensions, corresponding to a consistent formulation of the interaction of D3 branes with recoiling D particles, which are allowed to fluctuate independently only on the D3-brane hypersurface.Comment: 25 pages LaTeX, 4 eps figures include

Evaluations of topological Tutte polynomials

We find new properties of the topological transition polynomial of embedded graphs, $Q(G)$. We use these properties to explain the striking similarities between certain evaluations of Bollob\'as and Riordan's ribbon graph polynomial, $R(G)$, and the topological Penrose polynomial, $P(G)$. The general framework provided by $Q(G)$ also leads to several other combinatorial interpretations these polynomials. In particular, we express $P(G)$, $R(G)$, and the Tutte polynomial, $T(G)$, as sums of chromatic polynomials of graphs derived from $G$; show that these polynomials count $k$-valuations of medial graphs; show that $R(G)$ counts edge 3-colourings; and reformulate the Four Colour Theorem in terms of $R(G)$. We conclude with a reduction formula for the transition polynomial of the tensor product of two embedded graphs, showing that it leads to additional relations among these polynomials and to further combinatorial interpretations of $P(G)$ and $R(G)$.Comment: V2: major revision, several new results, and improved expositio

A supersymmetric D-brane Model of Space-Time Foam

We present a supersymmetric model of space-time foam with two stacks of eight D8-branes with equal string tensions, separated by a single bulk dimension containing D0-brane particles that represent quantum fluctuations in the space-time foam. The ground state configuration with static D-branes has zero vacuum energy. However, gravitons and other closed-string states propagating through the bulk may interact with the D0-particles, causing them to recoil and the vacuum energy to become non zero. This provides a possible origin of dark energy. Recoil also distorts the background metric felt by energetic massless string states, which travel at less than the usual (low-energy) velocity of light. On the other hand, the propagation of chiral matter anchored on the D8 branes is not affected by such space-time foam effects.Comment: 33 pages, latex, five figure

The status of traditional Scottish animal breeds and plant varieties and the implications for biodiversity

The aim of this scoping study was to evaluate the effects on Scottish biodiversity of changes in the use of traditional breeds and varieties. The overall objectives were: a) The evaluation of the importance of genetic loss from the reduction in use of these breeds and varieties, for example, the loss of unusual characteristics that might have been of particular local use. b) An assessment of the impacts of reduction in the ability to conduct further breeding or research on rare and traditional varieties and breeds. c) Identification of the loss of certain farming techniques associated with particular varieties and breeds. d) An assessment of possible losses of biodiversity associated with reduction in the use of these breeds and varieties and the farming systems associated with them

Quantum-Gravitational Diffusion and Stochastic Fluctuations in the Velocity of Light

We argue that quantum-gravitational fluctuations in the space-time background give the vacuum non-trivial optical properties that include diffusion and consequent uncertainties in the arrival times of photons, causing stochastic fluctuations in the velocity of light ``in vacuo''. Our proposal is motivated within a Liouville string formulation of quantum gravity that also suggests a frequency-dependent refractive index of the particle vacuum. We construct an explicit realization by treating photon propagation through quantum excitations of $D$-brane fluctuations in the space-time foam. These are described by higher-genus string effects, that lead to stochastic fluctuations in couplings, and hence in the velocity of light. We discuss the possibilities of constraining or measuring photon diffusion ``in vacuo'' via $\gamma$-ray observations of distant astrophysical sources.Comment: 17 pages LATEX, uses axodraw style fil

Space-Time Foam may Violate the Principle of Equivalence

The interactions of different particle species with the foamy space-time fluctuations expected in quantum gravity theories may not be universal, in which case different types of energetic particles may violate Lorentz invariance by varying amounts, violating the equivalence principle. We illustrate this possibility in two different models of space-time foam based on D-particle fluctuations in either flat Minkowski space or a stack of intersecting D-branes. Both models suggest that Lorentz invariance could be violated for energetic particles that do not carry conserved charges, such as photons, whereas charged particles such electrons would propagate in a Lorentz-inavariant way. The D-brane model further suggests that gluon propagation might violate Lorentz invariance, but not neutrinos. We argue that these conclusions hold at both the tree (lowest-genus) and loop (higher-genus) levels, and discuss their implications for the phenomenology of quantum gravity.Comment: 20 pages, 4 figures, the version accepted for publication in the International Journal of Modern Physics

Compactification and Supersymmetry Breaking in M-theory

Keeping N=1 supersymmetry in 4-dimension and in the leading order, we disuss the various orbifold compactifications of M-theory suggested by Horava and Witten on $T^6/Z_3$, $T^6/Z_6$, $T^6/Z_{12}$, and the compactification by keeping singlets under $SU(2)\times U(1)$ symmetry, then the compactification on $S^1/Z_2$. We also discuss the next to leading order K\"ahler potential, superpotential, and gauge kinetic function in the $Z_{12}$ case. In addition, we calculate the SUSY breaking soft terms and find out that the universality of the scalar masses will be violated, but the violation might be very small.Comment: 16 pages, latex, no figure

Test of the Additivity Principle for Current Fluctuations in a Model of Heat Conduction

The additivity principle allows to compute the current distribution in many one-dimensional (1D) nonequilibrium systems. Using simulations, we confirm this conjecture in the 1D Kipnis-Marchioro-Presutti model of heat conduction for a wide current interval. The current distribution shows both Gaussian and non-Gaussian regimes, and obeys the Gallavotti-Cohen fluctuation theorem. We verify the existence of a well-defined temperature profile associated to a given current fluctuation. This profile is independent of the sign of the current, and this symmetry extends to higher-order profiles and spatial correlations. We also show that finite-time joint fluctuations of the current and the profile are described by the additivity functional. These results suggest the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems.Comment: 4 pages, 4 figure