Supersymmetry Breakings and Fermat's Last Theorem
نویسنده
چکیده
A mechanism of supersymmetry breaking in two or four-dimensions is given, in which the breaking is related to the Fermat's last theorem. It is shown that supersymmetry is exact at some irrational number points in parameter space, while it is broken at all rational number points except for the origin. Accordingly, supersymmetry is exact almost everywhere, as well as broken almost everywhere on the real axis in the parameter space at the same time. This is the first explicit mechanism of supersymmetry breaking with an arbitrarily small change of parameters around any exact supersymmetric model, which is possibly useful for realistically small non-perturbative supersymmetry breakings in superstring model building. As a byproduct, we also give a convenient superpotential for supersymmetry breaking only for irrational number parameters. Our superpotential can be added as a " hidden " sector to other useful supersymmetric models.
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IH. S. Vandiver, "Fermat's Last Theorem," Am. Math. Mlonthly, 53, 567-568, 1946. 2 H. S. Vandiver, "The Relation of Some Data Obtained from Rapid Computing Machines to the Theory of Cyclotomic Fields, these PROCEEDINGS, 40, 474-480, 1954. 3H. S. Vandiver, "A Theorem of Kummer's concerning the Second Factor of the Class Number of a Cyclotomic Field," Bull. Am. Math. Soc., 35, 333-335, 1929. 4D. ...
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