153,991 research outputs found
Limits for circular Jacobi beta-ensembles
Bourgade, Nikeghbali and Rouault recently proposed a matrix model for the
circular Jacobi -ensemble, which is a generalization of the Dyson
circular -ensemble but equipped with an additional parameter , and
further studied its limiting spectral measure. We calculate the scaling limits
for expected products of characteristic polynomials of circular Jacobi
-ensembles. For the fixed constant , the resulting limit near the
spectrum singularity is proven to be a new multivariate function. When , the scaling limits in the bulk and at the soft edge agree with those of
the Hermite (Gaussian), Laguerre (Chiral) and Jacobi -ensembles proved
in the joint work with P Desrosiers "Asymptotics for products of characteristic
polynomials in classical beta-ensembles", Constr. Approx. 39 (2014),
arXiv:1112.1119v3. As corollaries, for even the scaling limits of point
correlation functions for the ensemble are given. Besides, a transition from
the spectrum singularity to the soft edge limit is observed as goes to
infinity. The positivity of two special multivariate hypergeometric functions,
which appear as one factor of the joint eigenvalue densities for spiked
Jacobi/Wishart -ensembles and Gaussian -ensembles with source,
will also be shown.Comment: 26 page
No-go for tree-level R-symmetry breaking
We show that in gauge mediation models with tree-level R-symmetry breaking
where supersymmetry and R-symmetries are broken by different fields, the
gaugino mass either vanishes at one loop or finds a contribution from
loop-level R-symmetry breaking. Thus tree-level R-symmetry breaking for
phenomenology is either no-go or redundant in the simplest type of models.
Including explicit messenger mass terms in the superpotential with a particular
R-charge arrangement is helpful to bypass the no-go theorem, and the resulting
gaugino mass is suppressed by the messenger mass scale.Comment: 8 pages, 7 figures; v2: discussion on Driac gauginos and references
added; v3: a section on bypassing the no-go added, R-charge notation changed;
v4: typos, EPJC pre-published versio
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