18,627 research outputs found

    Multiloop calculations in supersymmetric theories with the higher covariant derivative regularization

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    Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not self-consistent. A consistent regularization, which does not break the supersymmetry, is the higher covariant derivative regularization. However, the integrals obtained with this regularization can not be usually calculated analytically. We discuss application of this regularization to the calculations in supersymmetric theories. In particular, it is demonstrated that integrals defining the beta-function are possibly integrals of total derivatives. This feature allows to explain the origin of the exact NSVZ beta-function, relating the beta-function with the anomalous dimensions of the matter superfields. However, integrals for the anomalous dimension should be calculated numerically.Comment: 8 pages, contribution to ACAT 2011 proceeding

    Very Extended E8E_8 and A8A_8 at low levels, Gravity and Supergravity

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    We define a level for a large class of Lorentzian Kac-Moody algebras. Using this we find the representation content of very extended AD−3A_{D-3} and E8E_8 (i.e. E11E_{11}) at low levels in terms of AD−1A_{D-1} and A10A_{10} representations respectively. The results are consistent with the conjectured very extended A8A_8 and E11E_{11} symmetries of gravity and maximal supergravity theories given respectively in hep-th/0104081 and hep-th/0107209. We explain how these results provided further evidence for these conjectures.Comment: 16 pages, plain tex (equation 3.3 modified and one reference expanded

    Duality Symmetries and G^{+++} Theories

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    We show that the non-linear realisations of all the very extended algebras G^{+++}, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G_2^{+++} and we argue that the non-linear realisation of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables corrected, other minor changes, one appendix added, refs. added. Version published in Class. Quant. Gra

    Contribution of matter fields to the Gell-Mann-Low function for N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives

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    Contribution of matter fields to the Gell-Mann-Low function for N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives, is obtained using Schwinger-Dyson equations and Slavnov-Tailor identities. A possible deviation of the result from the corresponding contribution in the exact Novikov, Shifman, Vainshtein and Zakharov ÎČ\beta-function is discussed.Comment: 20 pages, 4 figure

    HypTrails: A Bayesian Approach for Comparing Hypotheses About Human Trails on the Web

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    When users interact with the Web today, they leave sequential digital trails on a massive scale. Examples of such human trails include Web navigation, sequences of online restaurant reviews, or online music play lists. Understanding the factors that drive the production of these trails can be useful for e.g., improving underlying network structures, predicting user clicks or enhancing recommendations. In this work, we present a general approach called HypTrails for comparing a set of hypotheses about human trails on the Web, where hypotheses represent beliefs about transitions between states. Our approach utilizes Markov chain models with Bayesian inference. The main idea is to incorporate hypotheses as informative Dirichlet priors and to leverage the sensitivity of Bayes factors on the prior for comparing hypotheses with each other. For eliciting Dirichlet priors from hypotheses, we present an adaption of the so-called (trial) roulette method. We demonstrate the general mechanics and applicability of HypTrails by performing experiments with (i) synthetic trails for which we control the mechanisms that have produced them and (ii) empirical trails stemming from different domains including website navigation, business reviews and online music played. Our work expands the repertoire of methods available for studying human trails on the Web.Comment: Published in the proceedings of WWW'1

    Observation of exchange Coulomb interactions in the quantum Hall state at nu=3

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    Coulomb exchange interactions of electrons in the nu=3 quantum Hall state are determined from two inter-Landau level spin-flip excitations measured by resonant inelastic light scattering. The two coupled collective excitations are linked to inter-Landau level spin-flip transitions arising from the N=0 and N=1 Landau levels. The strong repulsion between the two spin-flip modes in the long-wave limit is clearly manifested in spectra displaying Coulomb exchange contributions that are comparable to the exchange energy for the quantum Hall state at nu=1. Theoretical calculations within the Hartree-Fock approximation are in a good agreement with measured energies of spin-flip collective excitations.Comment: 5 pages, 3 figures, to appear in PRB Rapid Communication

    Probing the spin states of three interacting electrons in quantum dots

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    We observe a low-lying sharp spin mode of three interacting electrons in an array of nanofabricated AlGaAs/GaAs quantum dots by means of resonant inelastic light scattering. The finding is enabled by a suppression of the inhomogeneous contribution to the excitation spectra obtained by reducing the number of optically-probed quantum dots. Supported by configuration-interaction calculations we argue that the observed spin mode offers a direct probe of Stoner ferromagnetism in the simplest case of three interacting spin one-half fermions
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