328 research outputs found
An improved model of vector mesons in holographic QCD
We analyze the sector of dimension-three vector meson operators in the "hard
wall" model of holographic QCD, including the vector and axial currents, dual
to gauge fields in the bulk, and the tensor operator
, dual to a two-form field satisfying a complex
self-duality condition. The model includes the effect of chiral symmetry
breaking on vector mesons, that involves a coupling between the dual gauge
field and the two-form field. We compute the leading logarithmic terms in the
operator product expansion of two-point functions and the leading
non-perturbative contribution to the tensor-vector correlator. The result is
consistent with the operator product expansion of QCD. We also study the
spectrum of vector mesons numerically.Comment: 19 page
Maximal quadratic modules on *-rings
We generalize the notion of and results on maximal proper quadratic modules
from commutative unital rings to -rings and discuss the relation of this
generalization to recent developments in noncommutative real algebraic
geometry. The simplest example of a maximal proper quadratic module is the cone
of all positive semidefinite complex matrices of a fixed dimension. We show
that the support of a maximal proper quadratic module is the symmetric part of
a prime -ideal, that every maximal proper quadratic module in a
Noetherian -ring comes from a maximal proper quadratic module in a simple
artinian ring with involution and that maximal proper quadratic modules satisfy
an intersection theorem. As an application we obtain the following extension of
Schm\" udgen's Strict Positivstellensatz for the Weyl algebra: Let be an
element of the Weyl algebra which is not negative semidefinite
in the Schr\" odinger representation. It is shown that under some conditions
there exists an integer and elements such
that is a finite sum of hermitian squares. This
result is not a proper generalization however because we don't have the bound
.Comment: 11 page
Quaternion-Octonion SU(3) Flavor Symmetry
Starting with the quaternionic formulation of isospin SU(2) group, we have
derived the relations for different components of isospin with quark states.
Extending this formalism to the case of SU(3) group we have considered the
theory of octonion variables. Accordingly, the octonion splitting of SU(3)
group have been reconsidered and various commutation relations for SU(3) group
and its shift operators are also derived and verified for different iso-spin
multiplets i.e. I, U and V- spins.
Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices
PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and
models of strong and electroweak interaction
Quaternion Octonion Reformulation of Quantum Chromodynamics
We have made an attempt to develop the quaternionic formulation of Yang -
Mill's field equations and octonion reformulation of quantum chromo dynamics
(QCD). Starting with the Lagrangian density, we have discussed the field
equations of SU(2) and SU(3) gauge fields for both cases of global and local
gauge symmetries. It has been shown that the three quaternion units explain the
structure of Yang- Mill's field while the seven octonion units provide the
consistent structure of SU(3)_{C} gauge symmetry of quantum chromo dynamics
Semi-invariants of symmetric quivers of finite type
Let be a symmetric quiver, where is a finite
quiver without oriented cycles and is a contravariant involution on
. The involution allows us to define a nondegenerate bilinear
form on a representation $V$ of $Q$. We shall call the representation
orthogonal if is symmetric and symplectic if is skew-symmetric.
Moreover we can define an action of products of classical groups on the space
of orthogonal representations and on the space of symplectic representations.
For symmetric quivers of finite type, we prove that the rings of
semi-invariants for this action are spanned by the semi-invariants of
determinantal type and, in the case when matrix defining is
skew-symmetric, by the Pfaffians
Dynamical Chiral Symmetry Breaking on the Light Front.II. The Nambu--Jona-Lasinio Model
An investigation of dynamical chiral symmetry breaking on the light front is
made in the Nambu--Jona-Lasinio model with one flavor and N colors. Analysis of
the model suffers from extraordinary complexity due to the existence of a
"fermionic constraint," i.e., a constraint equation for the bad spinor
component. However, to solve this constraint is of special importance. In
classical theory, we can exactly solve it and then explicitly check the
property of ``light-front chiral transformation.'' In quantum theory, we
introduce a bilocal formulation to solve the fermionic constraint by the 1/N
expansion. Systematic 1/N expansion of the fermion bilocal operator is realized
by the boson expansion method. The leading (bilocal) fermionic constraint
becomes a gap equation for a chiral condensate and thus if we choose a
nontrivial solution of the gap equation, we are in the broken phase. As a
result of the nonzero chiral condensate, we find unusual chiral transformation
of fields and nonvanishing of the light-front chiral charge. A leading order
eigenvalue equation for a single bosonic state is equivalent to a leading order
fermion-antifermion bound-state equation. We analytically solve it for scalar
and pseudoscalar mesons and obtain their light-cone wavefunctions and masses.
All of the results are entirely consistent with those of our previous analysis
on the chiral Yukawa model.Comment: 23 pages, REVTEX, the version to be published in Phys.Rev.D; Some
clarifications in discussion of the LC wavefunctions adde
Self-bound dense objects in holographic QCD
We study a self-bound dense object in the hard wall model. We consider a
spherically symmetric dense object which is characterized by its radial density
distribution and non-uniform but spherically symmetric chiral condensate. For
this we analytically solve the partial differential equations in the hard wall
model and read off the radial coordinate dependence of the density and chiral
condensate according to the AdS/CFT correspondence. We then attempt to describe
nucleon density profiles of a few nuclei within our framework and observe that
the confinement scale changes from a free nucleon to a nucleus. We briefly
discuss how to include the effect of higher dimensional operator into our
study. We finally comment on possible extensions of our work.Comment: 17 pages, 5 figures, figures replaced, minor revision, to appear in
JHE
Strongly Interacting Neutrinos and the Highest Energy Cosmic Rays
Cosmic rays of energies larger than the Greisen-Zatsepin-Kuzmin (GZK) cutoff
may be neutrinos if they acquire strong interactions due to a ``precocious
unification'' of forces. A scenario for this to happen is outlined. There is no
contradiction with precision measurements carried out at LEP and SLAC.
Observable consequences at LHC and future neutrino detectors are discussed.Comment: 9 pages, LaTeX2e, no macros, 2 eps. figures. Uses epsf.te
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