27 research outputs found
Perturbed nonlinear models from Noncommutativity
By means of the Ehrenfest's Theorem inside the context of a noncommutative
Quantum Mechanics it is obtained the Newton's Second Law in noncommutative
space. Considering discrete systems with infinite degrees of freedom whose
dynamical evolutions are governed by the noncommutative Newton's Second Law we
have constructed some alternative noncommutative generalizations of
two-dimensional field theories.Comment: 6 pages. v2 minor changes added and references adde
Abelian Toda field theories on the noncommutative plane
Generalizations of GL(n) abelian Toda and abelian affine
Toda field theories to the noncommutative plane are constructed. Our proposal
relies on the noncommutative extension of a zero-curvature condition satisfied
by algebra-valued gauge potentials dependent on the fields. This condition can
be expressed as noncommutative Leznov-Saveliev equations which make possible to
define the noncommutative generalizations as systems of second order
differential equations, with an infinite chain of conserved currents. The
actions corresponding to these field theories are also provided. The special
cases of GL(2) Liouville and sinh/sine-Gordon are
explicitly studied. It is also shown that from the noncommutative
(anti-)self-dual Yang-Mills equations in four dimensions it is possible to
obtain by dimensional reduction the equations of motion of the two-dimensional
models constructed. This fact supports the validity of the noncommutative
version of the Ward conjecture. The relation of our proposal to previous
versions of some specific Toda field theories reported in the literature is
presented as well.Comment: v3 30 pages, changes in the text, new sections included and
references adde
Noncommutative Integrable Field Theories in 2d
We study the noncommutative generalization of (euclidean) integrable models
in two-dimensions, specifically the sine- and sinh-Gordon and the U(N)
principal chiral models. By looking at tree-level amplitudes for the
sinh-Gordon model we show that its na\"\i ve noncommutative generalization is
{\em not} integrable. On the other hand, the addition of extra constraints,
obtained through the generalization of the zero-curvature method, renders the
model integrable. We construct explicit non-local non-trivial conserved charges
for the U(N) principal chiral model using the Brezin-Itzykson-Zinn-Justin-Zuber
method.Comment: 18 pages, 1 figure; v2: references adde
Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy
We propose an approach to the nonvanishing boundary value problem for
integrable hierarchies based on the dressing method. Then we apply the method
to the AKNS hierarchy. The solutions are found by introducing appropriate
vertex operators that takes into account the boundary conditions.Comment: Published version Proc. Quantum Theory and Symmetries 7
(QTS7)(Prague, Czech Republic, 2011
About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane
The relation of the noncommutative self-dual Chern-Simons (NCSDCS) system to
the noncommutative generalizations of Toda and of affine Toda field theories is
investigated more deeply. This paper continues the programme initiated in , where it was presented how it is possible to define Toda
field theories through second order differential equation systems starting from
the NCSDCS system. Here we show that using the connection of the NCSDCS to the
noncommutative chiral model, exact solutions of the Toda field theories can be
also constructed by means of the noncommutative extension of the uniton method
proposed in by Ki-Myeong Lee. Particularly some
specific solutions of the nc Liouville model are explicit constructed.Comment: 24 page
Multicharged Dyonic Integrable Models
We introduce and study new integrable models of A_n^{(1)}-Non-Abelian Toda
type which admit U(1)\otimes U(1) charged topological solitons. They correspond
to the symmetry breaking SU(n+1) \to SU(2)\otimes SU(2)\otimes U(1)^{n-2} and
are conjectured to describe charged dyonic domain walls of N=1 SU(n+1) SUSY
gauge theory in large n limit.
It is shown that this family of relativistic IMs corresponds to the first
negative grade q={-1} member of a dyonic hierarchy of generalized cKP type. The
explicit relation between the 1-soliton solutions (and the conserved charges as
well) of the IMs of grades q=-1 and q=2 is found. The properties of the IMs
corresponding to more general symmetry breaking SU(n+1) \to SU(2)^{\otimes
p}\otimes U(1)^{n-p} as well as IM with global SU(2) symmetries are discussed.Comment: 48pages, latex, v2. typos in eqns. (1.7) and (3.20) corrected, small
improvements in subsection 2.2, new reference added;v3. improvements in text
of Sect. 1,2 and 6; new Sect 7 and new refs. added; version to appear in
Nucl. Phys.
On negative flows of the AKNS hierarchy and a class of deformations of bihamiltonian structure of hydrodynamic type
A deformation parameter of a bihamiltonian structure of hydrodynamic type is
shown to parameterize different extensions of the AKNS hierarchy to include
negative flows. This construction establishes a purely algebraic link between,
on the one hand, two realizations of the first negative flow of the AKNS model
and, on the other, two-component generalizations of Camassa-Holm and Dym type
equations.
The two-component generalizations of Camassa-Holm and Dym type equations can
be obtained from the negative order Hamiltonians constructed from the Lenard
relations recursively applied on the Casimir of the first Poisson bracket of
hydrodynamic type. The positive order Hamiltonians, which follow from Lenard
scheme applied on the Casimir of the second Poisson bracket of hydrodynamic
type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS
Hamiltonians give rise to charges conserved with respect to equations of motion
of two-component Camassa-Holm and two-component Dym type equations.Comment: 20 pages, Late
T-Duality in 2-D Integrable Models
The non-conformal analog of abelian T-duality transformations relating pairs
of axial and vector integrable models from the non abelian affine Toda family
is constructed and studied in detail.Comment: 14 pages, Latex, v.2 misprints corrected, reference added, to appear
in J. Phys.