Nonperturbative effects in the electroweak theory and the baryon number generation

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H. Aoyama has been investigating construction of 2-fold supersymmetric model in three spatial dimensions. This investigation is an extention of his previous work on nonlinear supersymmetry, which he, with co-investigators, discovered while examining asymptotic behavior of the perturbative series in some quantum mechanical models and coined the term "N-fold supersymmetry". Much is known about the original one-dimensiocal case, less so in two-dimensions, and none whatsoever in three-dimension, since the said extended supersymmetry algebra induces set of complex nonlinear differential equations, which were quite difficult to solve. H. Aoyama has been working on this problem for the last few years and is close to completion of the complete construction and classification of the three dimensional models, which would have a wide varietry of applications, not to mention its noble theoretical status.S. Matsuda has been looking into the extra dimentsions. He has hyposized that the consmological … More constant comes from the Casimir energy of the extra dimensions and evaluated the size of the extra dimensions to be of order of sub-millimeter using the value of the cosmological constant obtained from WMAP. He has alos calculated the Casimir enery as a funcion of the moduli parameters in case the extra-dimensional space is atwo-dimensional torus. He also considered mini-blackhole creation predicted by extra-dimensional space and investigated a generalized uncertainty principle. This research will lead to better evaluation of the creation cross-secton of the mini-blackholes.K. Yamamoto has worked on extensions of the supersymmetric electroweak models, including lepton number generation, baryon number generation by motion of multi-dimensional scalar field, and its contribution to dark matter. In particular, he has studied motion of the multi-dimensional scalar field on the flat-space of the potential and found that it generates non-symmetric particle numbers effectively. This way, he has clarified relation between leption number generation and neutrino masses Less