362 research outputs found
General one-loop renormalization group evolutions and electroweak symmetry breaking in the (M+1)SSM
We study analytically the general features of electroweak symmetry breaking
in the context of the Minimal Supersymmetric Standard Model extended by one
Higgs singlet. The exact analytical forms of the renormalization group
evolutions of the Yukawa couplings and of the soft supersymmetry breaking
parameters are derived to one-loop order. They allow on one hand controllable
approximations in closed analytical form, and on the other a precise study of
the behaviour of infrared quasi fixed point regimes which we carry out. Some of
these regimes are shown to be phenomenologically inconsistent, leading to too
small an effective -parameter. The remaining ones serve as a suitable
benchmark to understand analytically some salient aspects, often noticed
numerically in the literature, in relation to the electroweak symmetry breaking
in this model. The study does not need any specific assumption on
or on boundary conditions for the soft supersymmetry breaking parameters, thus
allowing a general insight into the sensitivity of the low energy physics to
high energy assumptions.Comment: Latex, 41 pages, 7 figure
Fractional Supersymmetry and Infinite Dimensional Lie Algebras
In an earlier work extensions of supersymmetry and super Lie algebras were
constructed consistently starting from any representation \D of any Lie
algebra \g. Here it is shown how infinite dimensional Lie algebras appear
naturally within the framework of fractional supersymmetry. Using a
differential realization of \g this infinite dimensional Lie algebra,
containing the Lie algebra \g as a sub-algebra, is explicitly constructed.Comment: 8 pages, D.V.Volkov Memorial Conference ``Supersymmetry and Quantum
Field Theory'', Kharkov, July 25-29, 2000), two figure
Local Fractional Supersymmetry for Alternative Statistics
A group theory justification of one dimensional fractional supersymmetry is
proposed using an analogue of a coset space, just like the one introduced in
supersymmetry. This theory is then gauged to obtain a local fractional
supersymmetry {\it i.e.} a fractional supergravity which is then quantized {\it
\`a la Dirac} to obtain an equation of motion for a particle which is in a
representation of the braid group and should describe alternative statistics. A
formulation invariant under general reparametrization is given, by means of a
curved fractional superline.Comment: 15 pages, latex, no figur
Hopf algebras for ternary algebras
We construct an universal enveloping algebra associated to the ternary
extension of Lie (super)algebras called Lie algebra of order three. A
Poincar\'e-Birkhoff-Witt theorem is proven is this context. It this then shown
that this universal enveloping algebra can be endowed with a structure of Hopf
algebra. The study of the dual of the universal enveloping algebra enables to
define the parameters of the transformation of a Lie algebra of order three. It
turns out that these variables are the variables which generate the
three-exterior algebra.Comment: 21 page
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