10,174 research outputs found
Loop groups in Yang-Mills theory
We consider the Yang-Mills equations with a matrix gauge group on the de
Sitter dS, anti-de Sitter AdS and Minkowski spaces. On all
these spaces one can introduce a doubly warped metric in the form , where and are the functions of
and is the metric on the two-dimensional hyperbolic space .
We show that in the adiabatic limit, when the metric on is scaled down,
the Yang-Mills equations become the sigma-model equations describing harmonic
maps from a two-dimensional manifold (dS, AdS or ,
respectively) into the based loop group of
smooth maps from the boundary circle of into the gauge
group . From this correspondence and the implicit function theorem it
follows that the moduli space of Yang-Mills theory with a gauge group in
four dimensions is bijective to the moduli space of two-dimensional sigma model
with as the target space. The sigma-model field equations can be
reduced to equations of geodesics on , solutions of which yield
magnetic-type configurations of Yang-Mills fields. The group
naturally acts on their moduli space.Comment: 8 pages; v3: clarifying remarks and references adde
Does Finance Bolster Superstar Companies? Banks, Venture Capital, and Firm Size in Local U.S. Markets
We study the relative effect of venture capital and bank finance on large manufacturing firms in local U.S. markets. Theory predicts that with venture capital, the firm size distribution should become more stretched-out to the right, but it’s ambiguous on the effect of banks on large firms. The empirical evidence suggests that while the average size of firms in the top bin of the firm size distribution has remained unaffected by banking sector developments, it has increased with venture capital investment. We argue that this is due to the emergence of new corporate giants rather than the growth of existing ones. JEL Classification: G24, J24, L11banking, firm size, Venture Capital
Einstein-aether theory: Dynamics of relativistic particles with spin or polarization in a G\"odel-type universe
In the framework of the Einstein-aether theory we consider a cosmological
model, which describes the evolution of the unit dynamic vector field with
activated rotational degree of freedom. We discuss exact solutions of the
Einstein-aether theory, for which the space-time is of the G\"odel-type, the
velocity four-vector of the aether motion is characterized by a non-vanishing
vorticity, thus the rotational vectorial modes can be associated with the
source of the universe rotation. The main goal of our paper is to study the
motion of test relativistic particles with vectorial internal degree of freedom
(spin or polarization), which is coupled to the unit dynamic vector field. The
particles are considered as the test ones in the given space-time background of
the G\"odel-type; the spin (polarization) coupling to the unit dynamic vector
field is modeled using exact solutions of three types. The first exact solution
describes the aether with arbitrary Jacobson's coupling constants; the second
one relates to the case, when the Jacobson's constant responsible for the
vorticity is vanishing; the third exact solution is obtained using three
constraints for the coupling constants. The analysis of the exact expressions,
which are obtained for the particle momentum and for the spin (polarization)
four-vector components, shows that the interaction of the spin (polarization)
with the unit vector field induces a rotation, which is additional to the
geodesic precession of the spin (polarization) associated with the universe
rotation as a whole.Comment: 15 page
Closed N=2 Strings: Picture-Changing, Hidden Symmetries and SDG Hierarchy
We study the action of picture-changing and spectral flow operators on a
ground ring of ghost number zero operators in the chiral BRST cohomology of the
closed N=2 string and describe an infinite set of symmetry charges acting on
physical states. The transformations of physical string states are compared
with symmetries of self-dual gravity which is the effective field theory of the
closed N=2 string. We derive all infinitesimal symmetries of the self-dual
gravity equations in 2+2 dimensional spacetime and introduce an infinite
hierarchy of commuting flows on the moduli space of self-dual metrics. The
dependence on moduli parameters can be recovered by solving the equations of
the SDG hierarchy associated with an infinite set of abelian symmetries
generated recursively from translations. These non-local abelian symmetries are
shown to coincide with the hidden abelian string symmetries responsible for the
vanishing of most scattering amplitudes. Therefore, N=2 string theory
"predicts" not only self-dual gravity but also the SDG hierarchy.Comment: 41 pages, no figure
Neutrino eigenstates and flavour, spin and spin-flavour oscillations in a constant magnetic field
We further develop a recently proposed new approach to the description of the
relativistic neutrino flavour , spin
and spin-flavour oscillations in a constant magnetic field that is based on the use
of the exact neutrino stationary states in the magnetic field. The neutrino
flavour, spin and spin-flavour oscillations probabilities are calculated
accounting for the whole set of possible conversions between four neutrino
states. In general, the obtained expressions for the neutrino oscillations
probabilities exhibit new inherent features in the oscillation patterns. It is
shown, in particular, that: 1) in the presence of the transversal magnetic
field for a given choice of parameters (the energy and magnetic moments of
neutrinos and the strength of the magnetic field) the amplitude of the flavour
oscillations at the vacuum frequency is
modulated by the magnetic field frequency, 2) the neutrino spin oscillation
probability (without change of the neutrino flavour) exhibits the dependence on
the mass square difference . It is shown that the discussed
interplay of neutrino oscillations in magnetic fields on different frequencies
can have important consequences in astrophysical environments, in particular in
those peculiar for magnetars.Comment: 7 pages and 3 figures. arXiv admin note: text overlap with
arXiv:1803.0575
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