Prime divisors and divisorial ideals

AbstractLet I1,…,Ig be regular ideals in a Noetherian ring R. Then it is shown that there exist positive integers k1,…,kg such that (I1n1 + m1…Igng + mg):(I1m1…Igmg) = I1n1…Igng for all ni≥ki (i = 1,…,g) and for all nonnegative integers m1,...,mg. Using this, it is shown that if Δ is a multiplicatively closed set of nonzero ideals of R that satisfies certain hypotheses, then the sets Ass(R(I1n1…Igng)) equal for all large positive integers n1,...,ng. Also, if R is locally analytically unramified, then some related results for general sets Δ are proved

Self-Diffusion in Random-Tiling Quasicrystals

The first explicit realization of the conjecture that phason dynamics leads to self-diffusion in quasicrystals is presented for the icosahedral Ammann tilings. On short time scales, the transport is found to be subdiffusive with the exponent $\beta\approx0.57(1)$, while on long time scales it is consistent with normal diffusion that is up to an order of magnitude larger than in the typical room temperature vacancy-assisted self-diffusion. No simple finite-size scaling is found, suggesting anomalous corrections to normal diffusion, or existence of at least two independent length scales.Comment: 11 pages + 2 figures, COMPRESSED postscript figures available by anonymous ftp to black_hole.physics.ubc.ca directory outgoing/diffuse (use bi for binary mode to transfer), REVTeX 3.0, CTP-TAMU 21/9

R-mediation of Dynamical Supersymmetry Breaking

We propose a simple scenario of the dynamical supersymmetry breaking in four dimensional supergravity theories. The supersymmetry breaking sector is assumed to be completely separated as a sequestered sector from the visible sector, except for the communication by the gravity and U(1)_R gauge interactions, and the supersymmetry breaking is mediated by the superconformal anomaly and U(1)_R gauge interaction. Supersymmetry is dynamically broken by the interplay between the non-perturbative effect of the gauge interaction and Fayet-Iliopoulos D-term of U(1)_R which necessarily exists in supergravity theories with gauged U(1)_R symmetry. We construct an explicit model which gives phenomenologically acceptable mass spectrum of superpartners with vanishing (or very small) cosmological constant.Comment: 12 pages, to be published in Phys. Rev.

The Reach of the Fermilab Tevatron and CERN LHC for Gaugino Mediated SUSY Breaking Models

In supersymmetric models with gaugino mediated SUSY breaking (inoMSB), it is assumed that SUSY breaking on a hidden brane is communicated to the visible brane via gauge superfields which propagate in the bulk. This leads to GUT models where the common gaugino mass $m_{1/2}$ is the only soft SUSY breaking term to receive contributions at tree level. To obtain a viable phenomenology, it is assumed that the gaugino mass is induced at some scale $M_c$ beyond the GUT scale, and that additional renormalization group running takes place between $M_c$ and $M_{GUT}$ as in a SUSY GUT. We assume an SU(5) SUSY GUT above the GUT scale, and compute the SUSY particle spectrum expected in models with inoMSB. We use the Monte Carlo program ISAJET to simulate signals within the inoMSB model, and compute the SUSY reach including cuts and triggers approriate to Fermilab Tevatron and CERN LHC experiments. We find no reach for SUSY by the Tevatron collider in the trilepton channel. %either with or without %identified tau leptons. At the CERN LHC, values of $m_{1/2}=1000$ (1160) GeV can be probed with 10 (100) fb$^{-1}$ of integrated luminosity, corresponding to a reach in terms of $m_{\tg}$ of 2150 (2500) GeV. The inoMSB model and mSUGRA can likely only be differentiated at a linear $e^+e^-$ collider with sufficient energy to produce sleptons and charginos.Comment: 17 page revtex file with 9 PS figure

Twistor Strings with Flavour

We explore the tree-level description of a class of N=2 UV-finite SYM theories with fundamental flavour within a topological B-model twistor string framework. In particular, we identify the twistor dual of the Sp(N) gauge theory with one antisymmetric and four fundamental hypermultiplets, as well as that of the SU(N) theory with 2N hypermultiplets. This is achieved by suitably orientifolding/orbifolding the original N=4 setup of Witten and adding a certain number of new topological 'flavour'-branes at the orientifold/orbifold fixed planes to provide the fundamental matter. We further comment on the appearance of these objects in the B-model on CP(3|4). An interesting aspect of our construction is that, unlike the IIB description of these theories in terms of D3 and D7-branes, on the twistor side part of the global flavour symmetry is realised geometrically. We provide evidence for this correspondence by calculating and matching amplitudes on both sides.Comment: 38+12 pages; uses axodraw.sty. v2: References added, minor clarification

Mirror Manifolds in Higher Dimension

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and hence naturally generalize to other dimensions. The moduli spaces for Calabi--Yau $d$-folds are somewhat different from the ``special K\"ahler manifolds'' which had occurred for $d=3$, and we indicate the new geometrical structures which arise. We formulate and apply procedures which allow for the construction of mirror maps and the calculation of order-by-order instanton corrections to Yukawa couplings. Mathematically, these corrections are expected to correspond to calculating Chern classes of various parameter spaces (Hilbert schemes) for rational curves on Calabi--Yau manifolds. Our results agree with those obtained by more traditional mathematical methods in the limited number of cases for which the latter analysis can be carried out. Finally, we make explicit some striking relations between instanton corrections for various Yukawa couplings, derived from the associativity of the operator product algebra.Comment: 44 pages plus 3 tables using harvma

A Search for Correlation of Ultra-High Energy Cosmic Rays with IRAS-PSCz and 2MASS-6dF Galaxies

We study the arrival directions of 69 ultra-high energy cosmic rays (UHECRs) observed at the Pierre Auger Observatory (PAO) with energies exceeding 55 EeV. We investigate whether the UHECRs exhibit the anisotropy signal expected if the primary particles are protons that originate in galaxies in the local universe, or in sources correlated with these galaxies. We cross-correlate the UHECR arrival directions with the positions of IRAS-PSCz and 2MASS-6dF galaxies taking into account particle energy losses during propagation. This is the first time that the 6dF survey is used in a search for the sources of UHECRs and the first time that the PSCz survey is used with the full 69 PAO events. The observed cross-correlation signal is larger for the PAO UHECRs than for 94% (98%) of realisations from an isotropic distribution when cross-correlated with the PSCz (6dF). On the other hand the observed cross-correlation signal is lower than that expected from 85% of realisations, had the UHECRs originated in galaxies in either survey. The observed cross-correlation signal does exceed that expected by 50% of the realisations if the UHECRs are randomly deflected by intervening magnetic fields by 5 degrees or more. We propose a new method of analysing the expected anisotropy signal, by dividing the predicted UHECR source distribution into equal predicted flux radial shells, which can help localise and constrain the properties of UHECR sources. We find that the 69 PAO events are consistent with isotropy in the nearest of three shells we define, whereas there is weak evidence for correlation with the predicted source distribution in the two more distant shells in which the galaxy distribution is less anisotropic.Comment: 23 pages, version published in JCA

Counting BPS states on the Enriques Calabi-Yau

We study topological string amplitudes for the FHSV model using various techniques. This model has a type II realization involving a Calabi-Yau threefold with Enriques fibres, which we call the Enriques Calabi-Yau. By applying heterotic/type IIA duality, we compute the topological amplitudes in the fibre to all genera. It turns out that there are two different ways to do the computation that lead to topological couplings with different BPS content. One of them leads to the standard D0-D2 counting amplitudes, and from the other one we obtain information about bound states of D0-D4-D2 branes on the Enriques fibre. We also study the model using mirror symmetry and the holomorphic anomaly equations. We verify in this way the heterotic results for the D0-D2 generating functional for low genera and find closed expressions for the topological amplitudes on the total space in terms of modular forms, and up to genus four. This model turns out to be much simpler than the generic B-model and might be exactly solvable.Comment: 62 pages, v3: some results at genus 3 corrected, more typos correcte

Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections

We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2 quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur

Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics

When Lenz proposed a simple model for phase transitions in magnetism, he couldn't have imagined that the "Ising model" was to become a jewel in field of equilibrium statistical mechanics. Its role spans the spectrum, from a good pedagogical example to a universality class in critical phenomena. A quarter century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing a seemingly trivial modification to the Ising lattice gas, they took it into the vast realms of non-equilibrium statistical mechanics. An abundant variety of unexpected behavior emerged and caught many of us by surprise. We present a brief review of some of the new insights garnered and some of the outstanding puzzles, as well as speculate on the model's role in the future of non-equilibrium statistical physics.Comment: 3 figures. Proceedings of 100th Statistical Mechanics Meeting, Rutgers, NJ (December, 2008