98,754 research outputs found

    Eta invariants with spectral boundary conditions

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    We study the asymptotics of the heat trace \Tr\{fPe^{-tP^2}\} where PP is an operator of Dirac type, where ff is an auxiliary smooth smearing function which is used to localize the problem, and where we impose spectral boundary conditions. Using functorial techniques and special case calculations, the boundary part of the leading coefficients in the asymptotic expansion is found.Comment: 19 pages, LaTeX, extended Introductio

    Muon anomalous magnetic moment from effective supersymmetry

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    We present a detailed analysis on the possible maximal value of the muon (g-2) (= 2 a_mu) within the context of effective SUSY models with R parity conservation. First of all, the mixing among the second and the third family sleptons can contribute at one loop level to the a_mu(SUSY) and tau -> mu gamma simultaneously. One finds that the a_mu(SUSY) can be as large as (10-20)*10^-10 for any tan beta, imposing the upper limit on the tau -> mu gamma branching ratio. Furthermore, the two-loop Barr-Zee type contributions to a_mu(SUSY) can be significant for large tan beta, if a stop is light and mu and A_t are large enough (O(1) TeV). In this case, it is possible to have a_mu(SUSY) upto O(10)*10^-10 without conflicting with tau -> l gamma. We conclude that the possible maximal value for a_mu(SUSY) is about 20*10^-10 for any tan beta. Therefore the BNL experiment on the muon a_mu can exclude the effective SUSY models only if the measured deviation is larger than \sim 30*10^-10.Comment: 10 pages, 3 figure

    Universal curvature identities

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    We study scalar and symmetric 2-form valued universal curvature identities. We use this to establish the Gauss-Bonnet theorem using heat equation methods, to give a new proof of a result of Kuz'mina and Labbi concerning the Euler-Lagrange equations of the Gauss-Bonnet integral, and to give a new derivation of the Euh-Park-Sekigawa identity.Comment: 11 page

    Painlev\'{e} analysis of the coupled nonlinear Schr\"{o}dinger equation for polarized optical waves in an isotropic medium

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    Using the Painlev\'{e} analysis, we investigate the integrability properties of a system of two coupled nonlinear Schr\"{o}dinger equations that describe the propagation of orthogonally polarized optical waves in an isotropic medium. Besides the well-known integrable vector nonlinear Schr\"{o}dinger equation, we show that there exist a new set of equations passing the Painlev\'{e} test where the self and cross phase modulational terms are of different magnitude. We introduce the Hirota bilinearization and the B\"{a}cklund transformation to obtain soliton solutions and prove integrability by making a change of variables. The conditions on the third-order susceptibility tensor χ(3)\chi^{(3)} imposed by these new integrable equations are explained
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