arXiv subjects

S. Krivonos

Publications and source records attributed to S. Krivonos.

86 records · Page 5Linked to original sources

arXiv1995

On the Super-NLS Equation and its Relation with N=2 Super-KdV within Coset Approach

A manifestly $N=2$ supersymmetric coset formalism is introduced to describe integrable hierarchies. It is applied to analyze the super-NLS equation. It possesses an $N=2$ symmetry since it can be obtained from a manifest $N=2$ coset algebra construction. A remarkable result is here discussed: the existence of a Bäcklund transformation which connects the super-NLS equation to the equations belonging to the integrable hierarchy of one particular (the $a=4$) $N=2$ super-KdV equation. $N=2$ scalar Lax pair operators are introduced for both super-KdV and super-NLS.

hep-th↗

arXiv1995

THE MINIMAL N=2 SUPEREXTENSION OF THE NLS EQUATION

We show that the well known $N=1$ NLS equation possesses $N=2$ supersymmetry and thus it is actually the $N=2$ NLS equation. This supersymmetry is hidden in terms of the commonly used $N=1$ superfields but it becomes manifest after passing to the $N=2$ ones. In terms of the new defined variables the second Hamiltonian structure of the supersymmetric NLS equation coincides with the $N=2$ superconformal algebra and the $N=2$ NLS equation belongs to the $N=2$ $a=4$ KdV hierarchy. We propose the KP-like Lax operator in terms of the $N=2$ superfields which reproduces all the conserved currents for the corresponding hierarchy.

hep-th↗

arXiv1995

MORE ON THE LINEARIZATION OF $W$-ALGEBRAS

We show that a wide class of $W$-(super)algebras, including $W_N^{(N-1)}$, $U(N)$-superconformal as well as $W_N$ nonlinear algebras, can be linearized by embedding them as subalgebras into some {\em linear} (super)conformal algebras with finite sets of currents. The general construction is illustrated by the example of $W_4$ algebra.

hep-th↗

arXiv1995

The Full Structure of Quantum $N=2$ Super-$W_3^{(2)}$ Algebra

We present the complete structure of the nonlinear $N=2$ super extension of Polyakov-Bershadsky, $W_3^{(2)}$, algebra with the generic central charge, $c$, at the {\it quantum} level. It contains extra two pairs of fermionic currents with integer spins 1 and 2, besides the currents of $N=2$ superconformal and $W_3^{(2)}$ algebras. For $c\rightarrow \infty$ limit, the algebra reduces to the classical one, which has been studied previously. The 'hybrid' field realization of this algebra is also discussed.

hep-th↗

arXiv1994

Linearizing $W_{2,4}$ and $WB_2$ Algebras

It has recently been shown that the $W_3$ and $W_3^{(2)}$ algebras can be considered as subalgebras in some linear conformal algebras. In this paper we show that the nonlinear algebras $W_{2,4}$ and $WB_2$ as well as Zamolodchikov's spin $5/2$ superalgebra also can be embedded as subalgebras into some linear conformal algebras with a finite set of currents. These linear algebras give rise to new realizations of the nonlinear algebras which could be suitable in the construction of $W$-string theories.

hep-th↗

arXiv1994

Linearizing W-Algebras

We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras $W_3$ and $W_3^{(2)}$ can be embedded as subalgebras into some {\em linear} algebras with finite set of currents. Using these linear algebras we find new field realizations of $W_3^{(2)}$ and $W_3$ which could be a starting point for constructing new versions of $W$-string theories. We also reveal a number of hidden relationships between $W_3$ and $W_3^{(2)}$. We conjecture that similar linear algebras can exist for other $W$-algebras as well.

hep-th↗

arXiv1994

Nonlinear Realizations of the $W_3^{(2)}$ Algebra

In this letter we consider the nonlinear realizations of the classical Polyakov's algebra $W_3^{(2)}$. The coset space method and the covariant reduction procedure allow us to deduce the Boussinesq equation with interchanged space and evolution coordinates. By adding one more space coordinate and introducing two copies of the $W_3^{(2)}$ algebra, the same method yields the $sl(3,R)$ Toda lattice equations.

hep-th↗

arXiv1994

The $N=2$ Super-$W_3^{(2)}$ Algebra

We construct the nonlinear $N=2$ super-$W_3^{(2)}$ algebra with an arbitrary central charge at the classical level in the framework of Polyakov "soldering" procedure. It contains two non-intersecting subalgebras: $N=2$ superconformal algebra and $W_3^{(2)}$ and their closure gives the $N=2$ super-$W_3^{(2)}$ algebra. Besides the currents of $N=2$ superconformal and $W_3^{(2)}$ algebras, it comprises two pairs of fermionic currents with spins 1 and 2. The hybrid field realization and contractions to the zero central charge are constructed.

hep-th↗

arXiv1993

N=2 Super Boussinesq Hierarchy: Lax Pairs and Conservation Laws

We study the integrability properties of the one-parameter family of $N=2$ super Boussinesq equations obtained earlier by two of us (E.I. \& S.K., Phys. Lett. B 291 (1992) 63) as a hamiltonian flow on the $N=2$ super-$W_3$ algebra. We show that it admits nontrivial higher order conserved quantities and hence gives rise to integrable hierarchies only for three values of the involved parameter, $α=-2,\;-1/2,\;5/2$. We find that for the case $α= -1/2$ there exists a Lax pair formulation in terms of local $N=2$ pseudo-differential operators, while for $α= -2$ the associated equation turns out to be bi-hamiltonian.

hep-th↗

arXiv1993

N=2 Super - $W_{3}$ Algebra and N=2 Super Boussinesq Equations

We study classical $N=2$ super-$W_3$ algebra and its interplay with $N=2$ supersymmetric extensions of the Boussinesq equation in the framework of the nonlinear realization method and the inverse Higgs - covariant reduction approach. These techniques have been previously applied by us in the bosonic $W_3$ case to give a new geometric interpretation of the Boussinesq hierarchy. Here we deduce the most general $N=2$ super Boussinesq equation and two kinds of the modified $N=2$ super Boussinesq equations, as well as the super Miura maps relating these systems to each other, by applying the covariant reduction to certain coset manifolds of linear $N=2$ super-$W_3^{\infty}$ symmetry associated with $N=2$ super-$W_3$. We discuss the integrability properties of the equations obtained and their correspondence with the formulation based on the notion of the second hamiltonian structure.

hep-th↗

arXiv1992

N=3 Supersymmetric Extension of KdV Equation

We construct a one-parameter family of N=3 supersymmetric extensions of the KdV equation as a Hamiltonian flow on N=3 superconformal algebra and argue that it is non-integrable for any choice of the parameter. Then we propose a modified N=3 super KdV equation which possesses the higher order conserved quantities and so is a candidate for an integrable system. Upon reduction to N=2, it yields the recently discussed ``would-be integrable'' version of the N=2 super KdV equation. In the bosonic core it contains a coupled system of the KdV type equation and a three-component generalization of the mKdV equation. We give a Hamiltonian formulation of the new N=3 super KdV equation as a flow on some contraction of the direct sum of two N=3 superconformal algebras.

hep-th↗

arXiv1992

Boussinesq-type equations from nonlinear realizations of $W_3$

We construct new coset realizations of infinite-dimensional linear $W_3^{\infty}$ symmetry associated with Zamolodchikov's $W_3$ algebra which are different from the previously explored $sl_3$ Toda realization of $W_3^{\infty}$. We deduce the Boussinesq and modified Boussinesq equations as constraints on the geometry of the corresponding coset manifolds.The main characteristic features of these realizations are:i. Among the coset parameters there are the space and time coordinates $x$ and $t$ which enter the Boussinesq equations, all other coset parameters are regarded as fields depending on these coordinates;ii. The spin 2 and 3 currents of $W_3$ and two spin 1 $U(1)$ Kac- Moody currents as well as two spin 0 fields related to the $W_3$currents via Miura maps, come out as the only essential parameters-fields of these cosets. The remaining coset fields are covariantly expressed through them;iii.The Miura maps get a new geometric interpretation as $W_3^{\infty}$ covariant constraints which relate the above fields while passing from one coset manifold to another; iv. The Boussinesq equation and two kinds of the modified Boussinesq equations appear geometrically as the dynamical constraints accomplishing $W_3^{\infty}$ covariant reductions of original coset manifolds to their two-dimensional geodesic submanifolds;v. The zero-curvature representations for these equations arise automatically as a consequence of the covariant reduction. The approach proposed could provide a universal geometric description of the relationship between $W$-type algebras and integrable hierarchies.

hep-th↗

arXiv1992

Superfield Realizations of $N=2$ Super-$W_3$

We present a manifestly $N=2$ supersymmetric formulation of $N=2$ super-$W_3$ algebra (its classical version) in terms of the spin 1 and spin 2 supercurrents. Two closely related types of the Feigin-Fuchs representation for these supercurrents are found: via two chiral spin $\frac{1}{2}$ superfields generating $N=2$ extended $U(1)$ Kac-Moody algebras and via two free chiral spin 0 superfields. We also construct a one-parameter family of $N=2$ super Boussinesq equations for which $N=2$ super-$W_3$ provides the second hamiltonian structure.

hep-th↗

arXiv1992

Nonlinear realizations of $W_3$ symmetry

We deduce the $sl_{3}$ Toda realization of classical $W_3$ symmetry on two scalar fields in a geometric way, proceeding from a nonlinear realization of some associate higher-spin symmetry $W_{3}^{\infty}$. The Toda equations are recognized as the constraints singling out a two-dimensional fully geodesic subspace in the initial coset space of $W_{3}^{\infty}$. The proposed geometric approach can be extended to other nonlinear algebras and integrable systems.

hep-th↗