16,842 research outputs found

    Conformal Field Theories, Representations and Lattice Constructions

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    An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and Z2Z_2-twisted theories, H(Λ)H(\Lambda) and H~(Λ)\tilde H(\Lambda) respectively, which may be constructed from a suitable even Euclidean lattice Λ\Lambda. Similarly, one may construct lattices ΛC\Lambda_C and Λ~C\tilde\Lambda_C by analogous constructions from a doubly-even binary code CC. In the case when CC is self-dual, the corresponding lattices are also. Similarly, H(Λ)H(\Lambda) and H~(Λ)\tilde H(\Lambda) are self-dual if and only if Λ\Lambda is. We show that H(ΛC)H(\Lambda_C) has a natural ``triality'' structure, which induces an isomorphism H(Λ~C)H~(ΛC)H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C) and also a triality structure on H~(Λ~C)\tilde H(\tilde\Lambda_C). For CC the Golay code, Λ~C\tilde\Lambda_C is the Leech lattice, and the triality on H~(Λ~C)\tilde H(\tilde\Lambda_C) is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories H(Λ)H(\Lambda) and H~(Λ)\tilde H(\Lambda) with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.Comment: 65 page

    Proceedings of the MECA Workshop on The Evoluation of the Martian Atmosphere

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    Topics addressed include: Mars' volatile budget; climatic implications of martian channels; bulk composition of Mars; accreted water inventory; evolution of CO2; dust storms; nonlinear frost albedo feedback on Mars; martian atmospheric evolution; effects of asteroidal and cometary impacts; and water exchange between the regolith and the atmosphere/cap system over obliquity timescales

    Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals

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    We have discovered a new family of three-dimensional crystal sphere packings that are strictly jammed (i.e., mechanically stable) and yet possess an anomalously low density. This family constitutes an uncountably infinite number of crystal packings that are subpackings of the densest crystal packings and are characterized by a high concentration of self-avoiding "tunnels" (chains of vacancies) that permeate the structures. The fundamental geometric characteristics of these tunneled crystals command interest in their own right and are described here in some detail. These include the lattice vectors (that specify the packing configurations), coordination structure, Voronoi cells, and density fluctuations. The tunneled crystals are not only candidate structures for achieving the jamming threshold (lowest-density rigid packing), but may have substantially broader significance for condensed matter physics and materials science.Comment: 19 pages, 5 figure

    On the Relationship between the Uniqueness of the Moonshine Module and Monstrous Moonshine

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    We consider the relationship between the conjectured uniqueness of the Moonshine Module, V{\cal V}^\natural, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group Thompson series. We first discuss a family of possible ZnZ_n meromorphic orbifold constructions of V{\cal V}^\natural based on automorphisms of the Leech lattice compactified bosonic string. We reproduce the Thompson series for all 51 non-Fricke classes of the Monster group MM together with a new relationship between the centralisers of these classes and 51 corresponding Conway group centralisers (generalising a well-known relationship for 5 such classes). Assuming that V{\cal V}^\natural is unique, we then consider meromorphic orbifoldings of V{\cal V}^\natural and show that Monstrous Moonshine holds if and only if the only meromorphic orbifoldings of V{\cal V}^\natural give V{\cal V}^\natural itself or the Leech theory. This constraint on the meromorphic orbifoldings of V{\cal V}^\natural therefore relates Monstrous Moonshine to the uniqueness of V{\cal V}^\natural in a new way.Comment: 53 pages, PlainTex, DIAS-STP-93-0

    Steady state existence of passive vector fields under the Kraichnan model

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    The steady state existence problem for Kraichnan advected passive vector models is considered for isotropic and anisotropic initial values in arbitrary dimension. The model includes the magnetohydrodynamic (MHD) equations, linear pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition to reproducing the previously known results for the MHD and linear pressure model, we obtain the values of the Kraichnan model roughness parameter ξ\xi for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction

    COLA. III. Radio Detection of Active Galactic Nucleus in Compact Moderate Luminosity Infrared Galaxies

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    We present results from 4.8 GHz Very Large Array (VLA) and global very long baseline interferometry (VLBI) observations of the northern half of the moderate FIR luminosity (median L_(IR) = 10^(11.01) L_☉) COLA sample of star-forming galaxies. VLBI sources are detected in a high fraction (20/90) of the galaxies observed. The radio luminosities of these cores (~10^(21) W Hz^(–1)) are too large to be explained by radio supernovae or supernova remnants and we argue that they are instead powered by active galactic nuclei (AGNs). These sub-parsec scale radio cores are preferentially detected toward galaxies whose VLA maps show bright 100-500 parsec scale nuclear radio components. Since these latter structures tightly follow the FIR to radio-continuum correlation for star formation, we conclude that the AGN-powered VLBI sources are associated with compact nuclear starburst environments. The implications for possible starburst-AGN connections are discussed. The detected VLBI sources have a relatively narrow range of radio luminosity consistent with models in which intense compact Eddington-limited starbursts regulate the gas supply onto a central supermassive black hole. The high incidence of AGN radio cores in compact starbursts suggests little or no delay between the starburst phase and the onset of AGN activity

    Collapse models with non-white noises II: particle-density coupled noises

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    We continue the analysis of models of spontaneous wave function collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical "noise" field, with specified autocorrelator, is coupled to a local nonrelativistic particle density. We derive general results in this model for the rates of density matrix diagonalization and of state vector reduction, and show that (in the absence of decoherence) both processes are governed by essentially the same rate parameters. As an alternative route to our reduction results, we also derive the Fokker-Planck equations that correspond to the initial stochastic Schr\"odinger equation. For specific models of the noise autocorrelator, including ones motivated by the structure of thermal Green's functions, we discuss the qualitative and qantitative dependence on model parameters, with particular emphasis on possible cosmological sources of the noise field.Comment: Latex, 43 pages; versions 2&3 have minor editorial revision

    Dynamical state reduction in an EPR experiment

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    A model is developed to describe state reduction in an EPR experiment as a continuous, relativistically-invariant, dynamical process. The system under consideration consists of two entangled isospin particles each of which undergo isospin measurements at spacelike separated locations. The equations of motion take the form of stochastic differential equations. These equations are solved explicitly in terms of random variables with a priori known probability distribution in the physical probability measure. In the course of solving these equations a correspondence is made between the state reduction process and the problem of classical nonlinear filtering. It is shown that the solution is covariant, violates Bell inequalities, and does not permit superluminal signaling. It is demonstrated that the model is not governed by the Free Will Theorem and it is argued that the claims of Conway and Kochen, that there can be no relativistic theory providing a mechanism for state reduction, are false.Comment: 19 pages, 3 figure

    Interactive Search and Exploration in Online Discussion Forums Using Multimodal Embeddings

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    In this paper we present a novel interactive multimodal learning system, which facilitates search and exploration in large networks of social multimedia users. It allows the analyst to identify and select users of interest, and to find similar users in an interactive learning setting. Our approach is based on novel multimodal representations of users, words and concepts, which we simultaneously learn by deploying a general-purpose neural embedding model. We show these representations to be useful not only for categorizing users, but also for automatically generating user and community profiles. Inspired by traditional summarization approaches, we create the profiles by selecting diverse and representative content from all available modalities, i.e. the text, image and user modality. The usefulness of the approach is evaluated using artificial actors, which simulate user behavior in a relevance feedback scenario. Multiple experiments were conducted in order to evaluate the quality of our multimodal representations, to compare different embedding strategies, and to determine the importance of different modalities. We demonstrate the capabilities of the proposed approach on two different multimedia collections originating from the violent online extremism forum Stormfront and the microblogging platform Twitter, which are particularly interesting due to the high semantic level of the discussions they feature
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