12,049 research outputs found
Reexamination of a Bound on the Dirac Neutrino Magnetic Moment from the Supernova Neutrino Luminosity
The neutrino helicity-flip process under the conditions of the supernova core
is reinvestigated. Instead of the uniform ball model for the SN core used in
previous analyses, realistic models for radial distributions and time evolution
of physical parameters in the SN core are considered. A new upper bound on the
Dirac neutrino magnetic moment is obtained from the limit on the supernova core
luminosity for nu_R emission.Comment: 13 pages, LaTeX, 8 EPS figures, submitted to Int. J. Mod. Phys.
Quiver varieties and a noncommutative P²
To any finite group Γ ⊂ SL₂(ℂ) and each element t in the center of the group algebra
Of Γ we associate a category, Coh(ℙ²_(Γ, τ),ℙ¹). It is defined as a suitable quotient of the
category of graded modules over (a graded version of) the deformed preprojective algebra
introduced by Crawley-Boevey and Holland. The category Coh(ℙ²_(Γ, τ),ℙ¹) should be thought
of as the category of coherent sheaves on a ‘noncommutative projective space’, ℙ²_(Γ, τ), equipped
with a framing at ℙ¹, the line at infinity. Our first result establishes an isomorphism between
the moduli space of torsion free objects of Coh(ℙ²_(Γ, τ),ℙ¹) and the Nakajima quiver variety arising
from G via the McKay correspondence. We apply the above isomorphism to deduce a generalization
of the Crawley-Boevey and Holland conjecture, saying that the moduli space of ‘rank 1’
projective modules over the deformed preprojective algebra is isomorphic to a particular quiver
variety. This reduces, for Γ = {1}, to the recently obtained parametrisation of the isomorphism
classes of right ideals in the first Weyl algebra, A₁, by points of the Calogero–
Moser space, due to Cannings and Holland and Berest and Wilson. Our approach is algebraic
and is based on a monadic description of torsion free sheaves on ℙ²_(Γ, τ). It is totally different
from the one used by Berest and Wilson, involving τ-functions
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