41 research outputs found
Monomial transformations of the projective space
We prove that, over any field, the dimension of the indeterminacy locus of a
rational transformation of which is defined by monomials of the same
degree with no common factors is at least , provided that the
degree of as a map is not divisible by . This implies upper bounds on
the multidegree of
Tau anomalous magnetic moment form factor at Super B/Flavor factories
The proposed high-luminosity B/Flavor factories offer new opportunities for
the improved determination of the fundamental physical parameters of standard
heavy leptons. Compared to the electron or the muon case, the magnetic
properties of the lepton are largely unexplored. We show that the
electromagnetic properties of the , and in particular its magnetic form
factor, may be measured competitively in these facilities, using unpolarized or
polarized electron beams. Various observables of the 's produced on top
of the resonances, such as cross-section and normal polarization for
unpolarized electrons or longitudinal and transverse asymmetries for polarized
beams, can be combined in order to increase the sensitivity on the magnetic
moment form factor. In the case of polarized electrons, we identify a special
combination of transverse and longitudinal polarizations able to
disentangle this anomalous magnetic form factor from both the charge form
factor and the interference with the Z-mediating amplitude. For an integrated
luminosity of one could achieve a sensitivity of
about , which is several orders of magnitude below any other existing
high- or low-energy bound on the magnetic moment. Thus one may obtain a QED
test of this fundamental quantity to a few % precision.Comment: 20 pages, 4 figure
Chen-Ruan cohomology of ADE singularities
We study Ruan's \textit{cohomological crepant resolution conjecture} for
orbifolds with transversal ADE singularities. In the -case we compute both
the Chen-Ruan cohomology ring and the quantum corrected
cohomology ring . The former is achieved in general, the
later up to some additional, technical assumptions. We construct an explicit
isomorphism between and in the -case,
verifying Ruan's conjecture. In the -case, the family
is not defined for . This implies that
the conjecture should be slightly modified. We propose a new conjecture in the
-case which we prove in the -case by constructing an explicit
isomorphism.Comment: This is a short version of my Ph.D. Thesis math.AG/0510528. Version
2: chapters 2,3,4 and 5 has been rewritten using the language of groupoids; a
link with the classical McKay correpondence is given. International Journal
of Mathematics (to appear
Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations
We first review some invariant theoretic results about the finite subgroups
of SU(2) in a quick algebraic way by using the McKay correspondence and quantum
affine Cartan matrices. By the way it turns out that some parameters
(a,b,h;p,q,r) that one usually associates with such a group and hence with a
simply-laced Coxeter-Dynkin diagram have a meaningful definition for the
non-simply-laced diagrams, too, and as a byproduct we extend Saito's formula
for the determinant of the Cartan matrix to all cases. Returning to invariant
theory we show that for each irreducible representation i of a binary
tetrahedral, octahedral, or icosahedral group one can find a homomorphism into
a finite complex reflection group whose defining reflection representation
restricts to i.Comment: 19 page
Self-gravitating branes of codimension 4 in Lovelock gravity
We construct a familly of exact solutions of Lovelock equations describing
codimension four branes with discrete symmetry in the transverse space. Unlike
what is known from pure Einstein gravity, where such brane solutions of higher
codimension are singular, the solutions we find, for the complete Lovelock
theory, only present removable singularities. The latter account for a
localised tension-like energy-momentum tensor on the brane, in analogy with the
case of a codimension two self-gravitating cosmic string in pure Einstein
gravity. However, the solutions we discuss present two main distinctive
features : the tension of the brane receives corrections from the induced
curvature of the brane's worldsheet and, in a given Lovelock theory, the
spectrum of possible values of the tension is discrete. These solutions provide
a new framework for the study of higher codimension braneworlds.Comment: 22 page
Quivers from Matrix Factorizations
We discuss how matrix factorizations offer a practical method of computing
the quiver and associated superpotential for a hypersurface singularity. This
method also yields explicit geometrical interpretations of D-branes (i.e.,
quiver representations) on a resolution given in terms of Grassmannians. As an
example we analyze some non-toric singularities which are resolved by a single
CP1 but have "length" greater than one. These examples have a much richer
structure than conifolds. A picture is proposed that relates matrix
factorizations in Landau-Ginzburg theories to the way that matrix
factorizations are used in this paper to perform noncommutative resolutions.Comment: 33 pages, (minor changes
Higgs boson production in photon-photon collision at ILC: a comparative study in different little Higgs models
We study the process \gamma\gamma->h->bb_bar at ILC as a probe of different
little Higgs models, including the simplest little Higgs model (SLH), the
littlest Higgs model (LH), and two types of littlest Higgs models with T-parity
(LHT-I, LHT-II). Compared with the Standard Model (SM) prediction, the
production rate is found to be sizably altered in these little Higgs models
and, more interestingly, different models give different predictions. We find
that the production rate can be possibly enhanced only in the LHT-II for some
part of the parameter space, while in all other cases the rate is suppressed.
The suppression can be 10% in the LH and as much as 60% in both the SLH and the
LHT-I/LHT-II. The severe suppression in the SLH happens for a large \tan\beta
and a small m_h, in which the new decay mode h->\eta\eta (\eta is a light
pseudo-scalar) is dominant; while for the LHT-I/LHT-II the large suppression
occurs when f and m_h are both small so that the new decay mode h->A_H A_H is
dominant. Therefore, the precision measurement of such a production process at
the ILC will allow for a test of these models and even distinguish between
different scenarios.Comment: Version in JHEP (h-g-g & h-gamma-gamma expressions added
Chromomagnetic Dipole Moment of the Top Quark Revisited
We study the complete one-loop contributions to the chromagnetic dipole
moment of the top quark in the Standard Model, two Higgs doublet
models, topcolor assited technicolor models (TC2), 331 models and extended
models with a single extra dimension. We find that the SM predicts
and that the predictions of the other models are also
consitent with the constraints imposed on by low-energy
precision measurements.Comment: 20 pages, 5 figures, Updat