16,773 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
On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice
A new type of correlated disorder is shown to be responsible for the
appearance of extended electronic states in one-dimensional aperiodic systems
like the Thue-Morse lattice. Our analysis leads to an understanding of the
underlying reason for the extended states in this system, for which only
numerical evidence is available in the literature so far. The present work also
sheds light on the restrictive conditions under which the extended states are
supported by this lattice.Comment: 11 pages, LaTeX V2.09, 1 figure (available on request), to appear in
Physical Review Letter
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