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E. Ivanov

Publications and source records attributed to E. Ivanov.

At least 91 records · Page 5Linked to original sources
arXiv1997

N=2 Affine Superalgebras and Hamiltonian Reduction in N=2 Superspace

We construct N=2 affine current algebras for the superalgebras sl(n|n-1)^{(1)} in terms of N=2 supercurrents subjected to nonlinear constraints and discuss the general procedure of the hamiltonian reduction in N=2 superspace at the classical level. We consider in detail the simplest case of N=2 sl(2|1)^{(1)} and show how N=2 superconformal algebra in N=2 superspace follows via the hamiltonian reduction. Applying the hamiltonian reduction to the case of N=2 sl(3|2)^{(1)}, we find two new extended N=2 superconformal algebras in a manifestly supersymmetric N=2 superfield form. Decoupling of four component currents of dimension 1/2 in them yields, respectively, u(2|1) and u(3) Knizhnik-Bershadsky superconformal algebras. We also discuss how the N=2 superfield formulations of N=2 W_{3} and N=2 W_{3}^{(2)} superconformal algebras come out in this framework, as well as some unusual extended N=2 superconformal algebras containing constrained N=2 stress tensor and/or spin 0 supercurrents.

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arXiv1997

N=4 Super NLS-mKdV Hierarchies

N=2 extension of affine algebra $\hat{sl(2)\oplus u(1)}$ possesses a hidden global N=4 supersymmetry and provides a second hamiltonian structure for a new N=4 supersymmetric integrable hierarchy defined on N=2 affine supercurrents. This system is an N=4 extension of at once two hierarchies, N=2 NLS and N=2 mKdV ones. It is related to N=4 KdV hierarchy via a generalized Sugawara-Feigin-Fuks construction which relates N=2 $\hat{sl(2)\oplus u(1)}$ algebra to ``small'' N=4 SCA. We also find the underlying affine hierarchy for another integrable system with the N=4 SCA second hamiltonian structure, ``quasi'' N=4 KdV hierarchy. It respects only N=2 supersymmetry. For both new hierarchies we construct scalar Lax formulations. We speculate that any N=2 affine algebra admitting a quaternionic structure possesses N=4 supersymmetry and so can be used to produce N=4 supersymmetric hierarchies. This suggests a way of classifying all such hierarchies.

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arXiv1997

The massive spinning particle revisited

We propose a formulation of the massive spinning particle in terms of physical bosonic and fermionic fields only. We make use neither of auxiliary objects of the type of $γ_5$ nor of gauge fields. The model is to be used as a suitable starting point for a forthcoming study of the rigid superparticle.

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arXiv1996

New super KdV system with the N=4 SCA as the hamiltonian structure

We present a new integrable extension of the a=-2, N=2 SKdV hierarchy, with the "small" N=4 superconformal algebra (SCA) as the second hamiltonian structure. As distinct from the previously known N=4 supersymmetric KdV hierarchy associated with the same N=4 SCA, the new system respects only N=2 rigid supersymmetry. We give for it both matrix and scalar Lax formulations and consider its various integrable reductions which complete the list of known SKdV systems with the N=2 SCA as the second hamiltonian structure. We construct a generalized Miura transformation which relates our system to the $α= -2$, N=2 super Boussinesq hierarchy and, respectively, the ``small'' N=4 SCA to the N=2 W_3 superalgebra.

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arXiv1996

New Integrable Extensions of N=2 KdV and Boussinesq Hierarchies

We construct a new variety of $N=2$ supersymmetric integrable systems by junction of pseudo-differential superspace Lax operators for $a=4$, $N=2$ KdV and multi-component $N=2$ NLS hierarchies. As an important particular case, we obtain Lax operator for $N=4$ super KdV system. A similar extension of one of $N=2$ super Boussinesq hierarchies is given. We also present a minimal $N=4$ supersymmetric extension of the second flow of $N=4$ KdV hierarchy and comment on its possible integrability.

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arXiv1996

More on $(4,4)$ supermultiplets in $SU(2)\times SU(2)$ harmonic superspace

We define the $SU(2)\times SU(2)$ harmonic superspace analogs of tensor and nonlinear $(4,4)$, $2D$ supermultiplets. They are described by constrained analytic superfields and provide an off-shell formulation of a class of torsionful $(4,4)$ supersymmetric sigma models with abelian translational isometries on the bosonic target. We examine their relation to $(4,4)$ twisted multiplets and discuss different types of $(4,4)$ dualities associated with them. One of these dualities implies the standard abelian $T$-duality relations between the bosonic targets in the initial and dual sigma model actions. We show that $N=4$, $2D$ superconformal group admits a simple realization on the superfields introduced, and present a new superfield form of the $(4,4)$ $SU(2)\times U(1)$ WZNW action.

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arXiv1995

N=4 super KdV hierarchy in N=4 and N=2 superspaces

We present the results of further analysis of the integrability properties of the $N=4$ supersymmetric KdV equation deduced earlier by two of us (F.D. \& E.I.) as a hamiltonian flow on $N=4$ $SU(2)$ superconformal algebra in the harmonic $N=4$ superspace. To make this equation and the relevant hamiltonian structures more tractable, we reformulate it in the ordinary $N=4$ and further in $N=2$ superspaces. In $N=2$ superspace it is given by a coupled system of evolution equations for a general $N=2$ superfield and two chiral and antichiral superfields, and involves two independent real parameters, $a$ and $b$. We construct a few first bosonic conserved charges in involution, of dimensions from 1 to 6, and show that they exist only for the following choices of the parameters: (i) $a= 4, \;b=0$; (ii) $a= -2,\; b= -6$; (iii) $a= -2, \;b= 6$. The same values are needed for the relevant evolution equations to be bi-hamiltonian. We demonstrate that these three options are related via $SU(2)$ transformations and actually amount to the $SU(2)$ covariant integrability condition found in the harmonic superspace approach. Our results provide a strong evidence that the unique $N=4$ $SU(2)$ super KdV hierarchy exists. Upon reduction to $N=2$ KdV, the above three possibilities cease to be equivalent. They give rise to the $a=4$ and $a=-2$ $N=2$ KdV hierarchies, which thus prove to be different truncations of the single $N=4$ $SU(2)$ KdV one.

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arXiv1995

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

We present a manifestly $N=2$ supersymmetric formulation of $N=2$ super-$W_3^{(2)}$ algebra (its classical version) in terms of the spin 1 unconstrained supercurrent generating a $N=2$ superconformal subalgebra and the spins 1/2, 2 bosonic and spins 1/2, 2 fermionic constrained supercurrents. We consider a superfield reduction of $N=2$ super-$W_3^{(2)}$ to $N=2$ super-$W_3$ and construct a family of evolution equations for which $N=2$ super-$W_3^{(2)}$ provides the second hamiltonian structure.

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arXiv1994

Chiral fermion action with (8,0) worldsheet supersymmetry

We propose an action describing chiral fermions with an arbitrary gauge group and with manifest $(8,0)$ worldsheet supersymmetry. The form of the action is inspired by and adapted for completing the twistor-like formulation of the $D=10$ heterotic superstring.

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arXiv1994

Sigma Models in (4,4) Harmonic Superspace

We define basics of $(4,4)\;\; 2D$ harmonic superspace with two independent sets of $SU(2)$ harmonic variables and apply it to construct new superfield actions of $(4,4)$ supersymmetric two-dimensional sigma models with torsion and mutually commuting left and right complex structures, as well as of their massive deformations. We show that the generic off-shell sigma model action is the general action of constrained analytic superfields $q^{(1,1)}$ representing twisted $N=4$ multiplets in $(4,4)$ harmonic superspace. The massive term of $q^{(1,1)}$ is shown to be unique; it generates a scalar potential the form of which is determined by the metric on the target bosonic manifold. We discuss in detail $(4,4)$ supersymmetric group manifold $SU(2)\times U(1)$ WZNW sigma model and its Liouville deformation. A deep analogy of the relevant superconformally invariant analytic superfield action to that of the improved tensor $N=2\;\;4D$ multiplet is found. We define $(4,4)$ duality transformation and find new off-shell dual representations of the previously constructed actions via {\it unconstrained} analytic $(4,4)$ superfields. The dual representation suggests some hints of how to describe $(4,4)$ models with non-commuting complex structures in the harmonic superspace.

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arXiv1993

Superhamiltonian formalism for $2D$ $N=1,2$ theories

We show how to formulate $2$-dimensional supersymmetric $N=1,2$ theories, both massive and conformal, within a manifestly supersymmetric hamiltonian framework, via the introduction of a (super)-Poisson brackets structure defined on superfields. In this approach, as distinct from the previously known superfield hamiltonian formulations, the dynamics is not separated into two unrelated $2D$ light-cone superspaces, but is recovered by specifying boundary conditions at a given ``super-time" coordinate. So the approach proposed provides a natural generalization of canonical hamiltonian formalism. One of its interesting features is that the physical and auxiliary fields equations appear on equal footing as the Hamilton ones.

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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.

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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.

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arXiv1993

N=2 Superconformal Affine Liouville Theory

We present a new supersymmetric integrable model: the $N=2$ superconformal affine Liouville theory. It interpolates between the $N=2$ super Liouville and $N=2$ super sine-Gordon theories and possesses a Lax representation on the complex affine Kac-Moody superalgebra ${\hat {sl(2| 2)^{(1)}}}$. We show that the higher spin $W_{1+\infty}$-type symmetry algebra of ordinary conformal affine Liouville theory extends to a $N=2\; W_{1/2 + \infty}$-type superalgebra.

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arXiv1993

$N=4$ super KdV equation

We construct $N=4$ supersymmetric KdV equation as a hamiltonian flow on the $N=4\;SU(2)$ super Virasoro algebra. The $N=4$ KdV superfield, the hamiltonian and the related Poisson structure are concisely formulated in $1D \;N=4$ harmonic superspace. The most general hamiltonian is shown to necessarily involve $SU(2)$ breaking parameters which are combined in a traceless rank 2 $SU(2)$ tensor. First nontrivial conserved charges of $N=4$ super KdV (of dimensions 2 and 4) are found to exist if and only if the $SU(2)$ breaking tensor is a bilinear of some $SU(2)$ vector with a fixed length proportional to the inverse of the central charge of $N=4\;SU(2)$ algebra. After the reduction to $N=2$ this restricted version of $N=4$ super KdV goes over to the $a=4$ integrable case of $N=2$ super KdV and so is expected to be integrable. We show that it is bi-hamiltonian like its $N=2$ prototype.

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arXiv1992

Harmonic space and quaternionic manifolds

We find a principle of harmonic analyticity underlying the quaternionic (quaternion-Kähler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is extended to a bi-harmonic space. The latter includes additional harmonic coordinates associated with both the tangent local $Sp(1)$ group and an extra rigid $SU(2)$ group rotating the complex structures. Then the constraints can be rewritten as integrability conditions for the existence of an analytic subspace in the bi-harmonic space and solved in terms of two unconstrained potentials on the analytic subspace. Geometrically, the potentials have the meaning of vielbeins associated with the harmonic coordinates. We also establish a one-to-one correspondence between the quaternionic spaces and off-shell $N=2$ supersymmetric sigma-models coupled to $N=2$ supergravity. The general $N=2$ sigma-model Lagrangian when written in the harmonic superspace is composed of the quaternionic potentials. Coordinates of the analytic subspace are identified with superfields describing $N=2$ matter hypermultiplets and a compensating hypermultiplet of $N=2$ supergravity. As an illustration we present the potentials for the symmetric quaternionic spaces.

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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.

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