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 $r$ fields, $r$ is the rank of the underlying Lie algebra. Most of the theories admit reduction, in which the equation is satisfied by fewer than $r$ 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 $a_{2n}^{(2)}$ that is the theory cannot have a further dimension $m$ reduction where $m<n$.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 $1+1$ 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$\sigma^*$ and $\phi$ in order to describe the interaction of$s$-quarks in hyperonic matter in the framework of the modifiedquark-meson coupling model. The coupling constant $g'^{B_K}_\sigma$in the density-dependent bag constant $B(\sigma)$ 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 $K^-$ and theequation of state for neutron star matter. The results show thatkaon condensation in hyperonic matter is sensitive to the $s$-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