4,709 research outputs found
Purely transmitting integrable defects
Some aspects of integrable field theories possessing purely transmitting
defects are described. The main example is the sine-Gordon model and several
striking features of a classical field theory containing one or more defects
are pointed out. Similar features appearing in the associated quantum field
theory are also reviewed briefly.Comment: 6 pages, to appear in Proceedings of the XVth International
Colloquium on Integrable Systems and Quantum Symmetries, Prague, June 200
Parafermionic Representation of the Affine Algebra at Fractional Level
The four fermionic currents of the affine superalgebra at
fractional level , u positive integer, are shown to be realised in
terms of a free scalar field, an doublet field and a primary field of
the parafermionic algebra .Comment: 5 pages, Latex 2
On a systematic approach to defects in classical integrable field theories
We present an inverse scattering approach to defects in classical integrable
field theories. Integrability is proved systematically by constructing the
generating function of the infinite set of modified integrals of motion. The
contribution of the defect to all orders is explicitely identified in terms of
a defect matrix. The underlying geometric picture is that those defects
correspond to Backlund transformations localized at a given point. A
classification of defect matrices as well as the corresponding defect
conditions is performed. The method is applied to a collection of well-known
integrable models and previous results are recovered (and extended) directly as
special cases. Finally, a brief discussion of the classical -matrix approach
in this context shows the relation to inhomogeneous lattice models and the need
to resort to lattice regularizations of integrable field theories with defects.Comment: 27 pages, no figures. Final version accepted for publication.
References added and section 5 amende
On a_2^(1) Reflection Matrices and Affine Toda Theories
We construct new non-diagonal solutions to the boundary Yang-Baxter-Equation
corresponding to a two-dimensional field theory with U_q(a_2^(1)) quantum
affine symmetry on a half-line. The requirements of boundary unitarity and
boundary crossing symmetry are then used to find overall scalar factors which
lead to consistent reflection matrices. Using the boundary bootstrap equations
we also compute the reflection factors for scalar bound states (breathers).
These breathers are expected to be identified with the fundamental quantum
particles in a_2^(1) affine Toda field theory and we therefore obtain a
conjecture for the affine Toda reflection factors. We compare these factors
with known classical results and discuss their duality properties and their
connections with particular boundary conditions.Comment: 34 pages, 4 figures, Latex2e, mistake in App. A corrected, some
references adde
Integrable Field Theories with Defects
The structure of integrable field theories in the presence of defects is
discussed in terms of boundary functions under the Lagrangian formalism.
Explicit examples of bosonic and fermionic theories are considered. In
particular, the boundary functions for the super sinh-Gordon model is
constructed and shown to generate the Backlund transformations for its soliton
solutions.Comment: talk presented at the XVth International Colloquium on Integrable
Systems and Quantum Symmetries, to appear in Czechoslovak Journal of Physics
(2006
Admissible sl(2/1) Characters and Parafermions
The branching functions of the affine superalgebra characters into
characters of the affine subalgebra are calculated for fractional
levels , u positive integer. They involve rational torus
and parafermion characters.Comment: 14 pages, Latex 2
Characters of admissible representations of the affine superalgebra sl(2|1)
We calculate characters and supercharacters for irreducible, admissible representations of the affine superalgebra sl(2|1) in both the Ramond and Neveu-Schwarz sectors and discuss their modular properties in the special case of level k=-1/2. We also show that the non-degenerate integrable characters coincide with some N=4 superconformal characters
Unconventional cosmology on the (thick) brane
We consider the cosmology of a thick codimension 1 brane. We obtain the
matching conditions leading to the cosmological evolution equations and show
that when one includes matter with a pressure component along the extra
dimension in the brane energy-momentum tensor, the cosmology is of non-standard
type. In particular one can get acceleration when a dust of non-relativistic
matter particles is the only source for the (modified) Friedman equation. Our
equations would seem to violate the conservation of energy-momentum from a 4D
perspective, but in 5D the energy-momentum is conserved. One could write down
an effective conserved 4D energy-momentum tensor attaching a ``dark energy''
component to the energy-momentum tensor of matter that has pressure along the
extra dimension. This extra component could, on a cosmological scale, be
interpreted as matter-coupled quintessence. We comment on the effective 4D
description of this effect in terms of the time evolution of a scalar field
(the 5D radion) coupled to this kind of matter.Comment: 9 pages, v2. eq.(17) corrected, comments on effective theory change
Null vectors, 3-point and 4-point functions in conformal field theory
We consider 3-point and 4-point correlation functions in a conformal field
theory with a W-algebra symmetry. Whereas in a theory with only Virasoro
symmetry the three point functions of descendants fields are uniquely
determined by the three point function of the corresponding primary fields this
is not the case for a theory with algebra symmetry. The generic 3-point
functions of W-descendant fields have a countable degree of arbitrariness. We
find, however, that if one of the fields belongs to a representation with null
states that this has implications for the 3-point functions. In particular if
one of the representations is doubly-degenerate then the 3-point function is
determined up to an overall constant. We extend our analysis to 4-point
functions and find that if two of the W-primary fields are doubly degenerate
then the intermediate channels are limited to a finite set and that the
corresponding chiral blocks are determined up to an overall constant. This
corresponds to the existence of a linear differential equation for the chiral
blocks with two completely degenerate fields as has been found in the work of
Bajnok~et~al.Comment: 10 pages, LaTeX 2.09, DAMTP-93-4
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