401 research outputs found
Helly dimension of algebraic groups
It is shown that for a linear algebraic group G over a field of
characteristic zero, there is a natural number \kappa(G) such that if a system
of Zariski closed cosets in G has empty intersection, then there is a subsystem
consisting of at most \kappa(G) cosets with empty intersection. This is applied
to the study of algebraic group actions on product varieties.Comment: 18 page
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
Normal mode splitting and mechanical effects of an optical lattice in a ring cavity
A novel regime of atom-cavity physics is explored, arising when large atom
samples dispersively interact with high-finesse optical cavities. A stable far
detuned optical lattice of several million rubidium atoms is formed inside an
optical ring resonator by coupling equal amounts of laser light to each
propagation direction of a longitudinal cavity mode. An adjacent longitudinal
mode, detunedby about 3 GHz, is used to perform probe transmission spectroscopy
of the system. The atom-cavity coupling for the lattice beams and the probe is
dispersive and dissipation results only from the finite photon-storage time.
The observation of two well-resolved normal modes demonstrates the regime of
strong cooperative coupling. The details of the normal mode spectrum reveal
mechanical effects associated with the retroaction of the probe upon the
optical lattice.Comment: 4 pages, 3 figure
Baryon Number-Induced Chern-Simons Couplings of Vector and Axial-Vector Mesons in Holographic QCD
We show that holographic models of QCD predict the presence of a Chern-Simons
coupling between vector and axial-vector mesons at finite baryon density. In
the AdS/CFT dictionary, the coefficient of this coupling is proportional to the
baryon number density, and is fixed uniquely in the five-dimensional
holographic dual by anomalies in the flavor currents. For the lightest mesons,
the coupling mixes transverse and polarization states. At
sufficiently large baryon number densities, it produces an instability, which
causes the and mesons to condense in a state breaking both
rotational and translational invariance.Comment: 4 page
Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds
We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold,
where the L^2 norm of all second derivatives of the function involving
horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian.
Perturbation allows us to get a-priori bounds for solutions to sub-elliptic PDE
in non-divergence form with bounded measurable coefficients. The method of
proof is through a Bochner technique. The Heisenberg group is seen to be en
extremal manifold for our inequality in the class of manifolds whose Ricci
curvature is non-negative.Comment: 13 page
Setting the scale of the p p and p bar p total cross sections using AdS/QCD
This paper is an addendum to our earlier paper \cite{pom} where we computed
the Pomeron contribution to and scattering in AdS/QCD. The
model of \cite{pom} depends on four parameters: the slope and intercept of the
Pomeron trajectory , a mass scale which
determines a form factor entering into matrix elements of the energy-momentum
tensor, and a coupling between the lightest spin
glueball and the proton which sets the overall scale of the total cross
section. Here we perform a more detailed computation of in
the Sakai-Sugimoto model using the construction of nucleons as instantons of
the dual 5d gauge theory and an effective 5d fermion description of these
nucleons which has been successfully used to compute a variety of nucleon-meson
couplings. We find
which is in reasonable agreement with the value determined by fitting single Pomeron exchange to data.Comment: 8 page
Lepton pairs from thermal mesons
We study the net dielectron production rates from an ensemble of thermal
mesons, using an effective Lagrangian to model their interaction. The coupling
between the electromagnetic and the hadronic sectors is done through the vector
meson dominance approach. For the first time, a complete set of light mesons is
considered. We include contributions from decays of the type
V~(PS)~~PS~(V)~+~, where V is a vector meson and PS is a
pseudoscalar, as well as those from binary reactions PS~+~PS, V~+~V, and
V~+~PS~. Direct decays of the type V~
are included and shown to be important. We find that the dielectron invariant
mass spectrum naturally divides in distinct regions: in the low mass domain the
decays from vector and pseudoscalar mesons form the dominant contribution. The
pion--pion annihilation and direct decays then pick up and form the leading
signal in an invariant mass region that includes the complex
and extends up to the . Above invariant mass ~1~GeV other
two-body reactions take over as the prominent mechanisms for lepton pair
generation. These facts will have quantitative bearing on the eventual
identification of the quark--gluon plasma.Comment: In ReVTeX 3.0, 9 figs. available from above email address. McGill
93/8, TPI-MINN-93/19-
Prospects for the cavity-assisted laser cooling of molecules
Cooling of molecules via free-space dissipative scattering of photons is
thought not to be practicable due to the inherently large number of Raman loss
channels available to molecules and the prohibitive expense of building
multiple repumping laser systems. The use of an optical cavity to enhance
coherent Rayleigh scattering into a decaying cavity mode has been suggested as
a potential method to mitigate Raman loss, thereby enabling the laser cooling
of molecules to ultracold temperatures. We discuss the possibility of
cavity-assisted laser cooling particles without closed transitions, identify
conditions necessary to achieve efficient cooling, and suggest solutions given
experimental constraints. Specifically, it is shown that cooperativities much
greater than unity are required for cooling without loss, and that this could
be achieved via the superradiant scattering associated with intracavity
self-localization of the molecules. Particular emphasis is given to the polar
hydroxyl radical (OH), cold samples of which are readily obtained from Stark
deceleration.Comment: 18 pages, 10 figure
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