19,808 research outputs found
Non-canonical folding of Dynkin diagrams and reduction of affine Toda theories
The equation of motion of affine Toda field theory is a coupled equation for
fields, is the rank of the underlying Lie algebra. Most of the theories
admit reduction, in which the equation is satisfied by fewer than fields.
The reductions in the existing literature are achieved by identifying (folding)
the points in the Dynkin diagrams which are connected by symmetry
(automorphism). In this paper we present many new reductions. In other words
the symmetry of affine Dynkin diagrams could be extended and it leads to
non-canonical foldings. We investigate these reductions in detail and formulate
general rules for possible reductions. We will show that eventually most of the
theories end up in that is the theory cannot have a further
dimension reduction where .Comment: 26 pages, Latex2e, usepackage `graphics.sty', 15 figure
Instability of Solitons in imaginary coupling affine Toda Field Theory
Affine Toda field theory with a pure imaginary coupling constant is a
non-hermitian theory. Therefore the solutions of the equation of motion are
complex. However, in dimensions it has many soliton solutions with
remarkable properties, such as real total energy/momentum and mass. Several
authors calculated quantum mass corrections of the solitons by claiming these
solitons are stable. We show that there exists a large class of classical
solutions which develops singularity after a finite lapse of time. Stability
claims, in earlier literature, were made ignoring these solutions. Therefore we
believe that a formulation of quantum theory on a firmer basis is necessary in
general and for the quantum mass corrections of solitons, in particular.Comment: 17 pages, latex, no figure
Holographic classification of Topological Insulators and its 8-fold periodicity
Using generic properties of Clifford algebras in any spatial dimension, we
explicitly classify Dirac hamiltonians with zero modes protected by the
discrete symmetries of time-reversal, particle-hole symmetry, and chirality.
Assuming the boundary states of topological insulators are Dirac fermions, we
thereby holographically reproduce the Periodic Table of topological insulators
found by Kitaev and Ryu. et. al, without using topological invariants nor
K-theory. In addition we find candidate Z_2 topological insulators in classes
AI, AII in dimensions 0,4 mod 8 and in classes C, D in dimensions 2,6 mod 8.Comment: 19 pages, 4 Table
Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
A time-reversal invariant Kitaev-type model is introduced in which spins
(Dirac matrices) on the square lattice interact via anisotropic
nearest-neighbor and next-nearest-neighbor exchange interactions. The model is
exactly solved by mapping it onto a tight-binding model of free Majorana
fermions coupled with static Z_2 gauge fields. The Majorana fermion model can
be viewed as a model of time-reversal invariant superconductor and is
classified as a member of symmetry class DIII in the Altland-Zirnbauer
classification. The ground-state phase diagram has two topologically distinct
gapped phases which are distinguished by a Z_2 topological invariant. The
topologically nontrivial phase supports both a Kramers' pair of gapless
Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana
states bound to a 0-flux vortex in the \pi-flux background. Power-law decaying
correlation functions of spins along the edge are obtained by taking the
gapless Majorana edge modes into account. The model is also defined on the
one-dimension ladder, in which case again the ground-state phase diagram has
Z_2 trivial and non-trivial phases.Comment: 17 pages, 9 figure
Magnetic moment of hyperons in nuclear matter by using quark-meson coupling models
We calculate the magnetic moments of hyperons in dense nuclear matter by
using relativistic quark models. Hyperons are treated as MIT bags, and the
interactions are considered to be mediated by the exchange of scalar and vector
mesons which are approximated as mean fields. Model dependence is investigated
by using the quark-meson coupling model and the modified quark-meson coupling
model; in the former the bag constant is independent of density and in the
latter it depends on density. Both models give us the magnitudes of the
magnetic moments increasing with density for most octet baryons. But there is a
considerable model dependence in the values of the magnetic moments in dense
medium. The magnetic moments at the nuclear saturation density calculated by
the quark meson coupling model are only a few percents larger than those in
free space, but the magnetic moments from the modified quark meson coupling
model increase more than 10% for most hyperons. The correlations between the
bag radius of hyperons and the magnetic moments of hyperons in dense matter are
discussed.Comment: substantial changes in the text, submitted to PL
Neutron Stars with Bose-Einstein Condensation of Antikaons as MIT Bags
We investigate the properties of an antikaon in medium, regarding itas a MIT
bag. We first construct the MIT bag model for a kaon with and
in order to describe the interaction of-quarks in hyperonic matter in the
framework of the modifiedquark-meson coupling model. The coupling constant
in the density-dependent bag constant is treated
as afree parameter to reproduce the optical potential of a kaon in asymmetric
matter and all other couplings are determined by usingSU(6) symmetry and the
quark counting rule. With various values ofthe kaon potential, we calculate the
effective mass of a kaon inmedium to compare it with that of a point-like kaon.
We thencalculate the population of octet baryons, leptons and and
theequation of state for neutron star matter. The results show thatkaon
condensation in hyperonic matter is sensitive to the -quarkinteraction and
also to the way of treating the kaon. The mass andthe radius of a neutron star
are obtained by solving theTolmann-Oppenheimer-Volkoff equation.Comment: 14 figure
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