24,052 research outputs found
On the duality of three-dimensional superfield theories
Within the superfield approach, we consider the duality between the
supersymmetric Maxwell-Chern-Simons and self-dual theories in three spacetime
dimensions. Using a gauge embedding method, we construct the dual theory to the
self-dual model interacting with a matter superfield, which turns out to be not
the Maxwell-Chern-Simons theory coupled to matter, but a more complicated
model, with a ``restricted'' gauge invariance. We stress the difficulties in
dualizing the self-dual field coupled to matter into a theory with complete
gauge invariance. After that, we show that the duality, achieved between these
two models at the tree level, also holds up to the lowest order quantum
corrections.Comment: 18 pages,2 figures, revtex4, v2: corrected reference
The higher grading structure of the WKI hierarchy and the two-component short pulse equation
A higher grading affine algebraic construction of integrable hierarchies,
containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is
proposed. We show that a two-component generalization of the Sch\" afer-Wayne
short pulse equation arises quite naturally from the first negative flow of the
WKI hierarchy. Some novel integrable nonautonomous models are also proposed.
The conserved charges, both local and nonlocal, are obtained from the Riccati
form of the spectral problem. The loop-soliton solutions of the WKI hierarchy
are systematically constructed through gauge followed by reciprocal B\" acklund
transformation, establishing the precise connection between the whole WKI and
AKNS hierarchies. The connection between the short pulse equation with the
sine-Gordon model is extended to a correspondence between the two-component
short pulse equation and the Lund-Regge model
The algebraic structure behind the derivative nonlinear Schroedinger equation
The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schr\"
odinger equation (DNLSE) amongst others interesting and important nonlinear
integrable equations. In this paper, a general higher grading affine algebraic
construction of integrable hierarchies is proposed and the KN hierarchy is
established in terms of a Kac-Moody algebra and principal
gradation. In this form, our spectral problem is linear in the spectral
parameter. The positive and negative flows are derived, showing that some
interesting physical models arise from the same algebraic structure. For
instance, the DNLSE is obtained as the second positive, while the Mikhailov
model as the first negative flows, respectively. The equivalence between the
latter and the massive Thirring model is explicitly demonstrated also. The
algebraic dressing method is employed to construct soliton solutions in a
systematic manner for all members of the hierarchy. Finally, the equivalence of
the spectral problem introduced in this paper with the usual one, which is
quadratic in the spectral parameter, is achieved by setting a particular
automorphism of the affine algebra, which maps the homogeneous into principal
gradation.Comment: 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
All-loop finiteness of the two-dimensional noncommutative supersymmetric gauge theory
Within the superfield approach, we discuss two-dimensional noncommutative
super-QED. Its all-order finiteness is shown explicitly.Comment: 7 page
Negative Even Grade mKdV Hierarchy and its Soliton Solutions
In this paper we provide an algebraic construction for the negative even mKdV
hierarchy which gives rise to time evolutions associated to even graded Lie
algebraic structure. We propose a modification of the dressing method, in order
to incorporate a non-trivial vacuum configuration and construct a deformed
vertex operator for , that enable us to obtain explicit and
systematic solutions for the whole negative even grade equations
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