494 research outputs found
Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup
For an affine spherical homogeneous space G/H of a connected semisimple
algebraic group G, we consider the factorization morphism by the action on G/H
of a maximal unipotent subgroup of G. We prove that this morphism is
equidimensional if and only if the weight semigroup of G/H satisfies some
simple condition.Comment: v2: title and abstract changed; v3: 16 pages, minor correction
Difficulties of an Infrared Extension of Differential Renormalization
We investigate the possibility of generalizing differential renormalization
of D.Z.Freedman, K.Johnson and J.I.Latorre in an invariant fashion to theories
with infrared divergencies via an infrared operation.
Two-dimensional models and the four-dimensional theory
diagrams with exceptional momenta are used as examples, while dimensional
renormalization serves as a test scheme for comparison. We write the basic
differential identities of the method simultaneously in co-ordinate and
momentum space, introducing two scales which remove ultraviolet and infrared
singularities. The consistent set of Fourier-transformation formulae is
derived. However, the values for tadpole-type Feynman integrals in higher
orders of perturbation theory prove to be ambiguous, depending on the order of
evaluation of the subgraphs. In two dimensions, even earlier than this
ambiguity manifests itself, renormalization-group calculations based on
infrared extension of differential renormalization lead to incorrect results.
We conclude that the extended differential renormalization procedure does not
perform the infrared operation in a self-consistent way, as the
original recipe does the ultraviolet operation.Comment: (minor changes have been made to make clear that no infrared problems
occur in the original ultraviolet procedure of [1]; subsection 2.1 has been
added to outline the ideas a simple example), 26 pages, LaTeX, JINR preprint
E2-92-538, Dubna (Dec.1992
A Bethe Ansatz Study of Free Energy and Excitation Spectrum for Even Spin Fateev Zamolodchikov Model
A Bethe Ansatz study of a self dual Z_N spin model is undertaken for even
spin system. One has to solve a coupled system of Bethe Ansatz Equations (BAE)
involving zeroes of two families of transfer matrices. A numerical study on
finite size lattices is done for identification of elementary excitations over
the Ferromagnetic and Antiferromagnetic ground states. The free energies for
both Ferromagnetic and Antiferromagnetic ground states and dispersion relation
for elementary excitations are found.Comment: 25 pages, 4 figure
Transcendental numbers and the topology of three-loop bubbles
We present a proof that all transcendental numbers that are needed for the
calculation of the master integrals for three-loop vacuum Feynman diagrams can
be obtained by calculating diagrams with an even simpler topology, the topology
of spectacles.Comment: 4 pages in REVTeX, 1 PostScript figure included, submitted to Phys.
Rev. Let
Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies
3D numerical studies have shown that the vertical voltage above the Baikal deep-water fault is detectable and that respective transfer functions, Ez-responses, are sensitive to the electrical resistivity changes of the fault, i.e.
these functions appear actually informative with respect to the resistivity «breath» of the fault. It means that if the fault resistivity changed, conventional electromagnetic instruments would be able to detect this fact by measurement
of the vertical electric field, Ez, or the vertical electric voltage just above the fault as well as horizontal magnetic field on the shore. Other electromagnetic field components (Ex, Ey, Hz) do not seem to be sensitive to the resistivity changes in such a thin fault (as wide as 500 m). On the other hand, such changes are thought to
be able to indicate a change of a stress state in the earthquake preparation zone. Besides, the vertical profile at the bottom of Lake Baikal is suitable for electromagnetic monitoring of the fault electrical resistivity changes.
Altogether, the vertical voltage above the deep-water fault might be one of earthquake precursors
Supersymmetric States in Large N Chern-Simons-Matter Theories
In this paper we study the spectrum of BPS operators/states in N=2
superconformal U(N) Chern-Simons-matter theories with adjoint chiral matter
fields, with and without superpotential. The superconformal indices and
conjectures on the full supersymmetric spectrum of the theories in the large N
limit with up to two adjoint matter fields are presented. Our results suggest
that some of these theories may have supergravity duals at strong coupling,
while some others may be dual to higher spin theories of gravity at strong
coupling. For the N=2 theory with no superpotential, we study the
renormalization of R-charge at finite 't Hooft coupling using "Z-minimization".
A particularly intriguing result is found in the case of one adjoint matter.Comment: 53 pages, 18 figures. v2: improved numerics, additional comments
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