98,754 research outputs found
Eta invariants with spectral boundary conditions
We study the asymptotics of the heat trace \Tr\{fPe^{-tP^2}\} where is
an operator of Dirac type, where 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
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
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
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 imposed by these new integrable equations are explained
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