arXiv subjects

S. Krivonos

Publications and source records attributed to S. Krivonos.

At least 73 records · Page 4Linked to original sources

arXiv1999

Partial breaking of N=1, D=10 supersymmetry

We describe the spontaneous partial breaking of $N=1 D=10$ supersymmetry to $N=(1,0) d=6$ and its dimensionally-reduced versions in the framework of the nonlinear realizations method. The basic Goldstone superfield is $N=(1,0) d=6$ hypermultiplet superfield satisfying a nonlinear generalization of the standard hypermultiplet constraint. We interpret the generalized constraint as the manifestly worldvolume supersymmetric form of equations of motion of the Type I super 5-brane in D=10. The related issues we address are a possible existence of brane extension of off-shell hypermultiplet actions, the possibility to utilize vector $N=(1,0) d=6$ supermultiplet as the Goldstone one, and the description of 1/4 breaking of $N=1 D=11$ supersymmetry.

hep-th↗

arXiv1999

N=1 D=4 supermembrane in the coset approach

$N=1 D=4$ supermembrane (in a flat background) and super D2-brane dual to it are described within the nonlinear realizations approach as theories of the partial supersymmetry breaking $N=1 D=4 \to N=1 d=3$. We construct the relevant invariant off-shell Goldstone superfield actions and demonstrate them to be dual to each other. Their bosonic cores are, respectively, the static-gauge Nambu-Goto and $d=3$ Born-Infeld actions. The supermembrane superfield equation of motion admits a transparent geometric interpretation suggesting an extension of the standard superembedding constraints. We briefly discuss the 1/4 breaking of $N=1 D=5$ supersymmetry along similar lines.

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arXiv1998

Partial breaking N=4 to N=2: hypermultiplet as a Goldstone superfield

We describe the partial breaking of $N=1 D=10$ supersymmetry down to $(1,0) d=6$ supersymmetry within the non-linear realization approach. The basic Goldstone superfield associated with this breaking is shown to be the $(1,0) d=6$ hypermultiplet superfield $q^{ia}$ subjected to a non-linear generalization of the standard hypermultiplet superfield constraint. The dynamical equations implied by this constraint are identified as the manifestly worldvolume supersymmetric equations of the Type I super 5-brane in D=10. We give arguments in favour of existence of an appropriate brane extension of off-shell hypermultiplet actions in harmonic superspace. Some related problems, in particular, the issue of utilizing other $(1,0) d=6$ supermultiplets as Goldstone ones, are shortly discussed.

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arXiv1998

Lax pairs for N=2,3 Supersymmetric KdV Equations and their Extensions

We present the Lax operator for the N=3 KdV hierarchy and consider its extensions. We also construct a new infinite family of N=2 supersymmetric hierarchies by exhibiting the corresponding super Lax operators. The new realization of N=4 supersymmetry on the two general N=2 superfields, bosonic spin 1 and fermionic spin 1/2, is discussed.

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arXiv1997

Extended N=2 supersymmetric matrix (1,s)-KdV hierarchies

We propose the Lax operators for N=2 supersymmetric matrix generalization of the bosonic (1,s)-KdV hierarchies. The simplest examples - the N=2 supersymmetric a=4 KdV and a=5/2 Boussinesq hierarchies - are discussed in detail.

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arXiv1997

Coset approach to the N=2 supersymmetric matrix GNLS hierarchies

We discuss a large class of coset constructions of the N=2 sl(n|n-1) affine superalgebra. We select admissible subalgebras, i.e. subalgebras that induce linear chiral/antichiral constraints on the coset supercurrents. We show that all the corresponding coset constructions lead to N=2 matrix GNLS hierarchies. We develop an algorithm to compute the relative Hamiltonians and flows. We spell out completely the case of the N=2 affine sl(3|2), which possesses four admissible subalgebras. The non-local second Hamiltonian structure of the N=2 matrix GNLS hierarchies is obtained via Dirac procedure from the local N=2 sl(n|n-1) affine superalgebra. We observe that to any second Hamiltonian structure with pure bosonic or pure fermionic superfield content there correspond two different N=2 matrix GNLS hierarchies.

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arXiv1997

The N=2 supersymmetric matrix GNLS hierarchies

We construct the matrix generalization of the N=2 supersymmetric GNLS hierarchies. This is done by exhibiting the corresponding matrix super Lax operators in terms of N=2 superfields in two different superfield bases. We present the second Hamiltonian structure and discrete symmetries. We then extend our discussion by conjecturing the Lax operators of different reductions of the N=2 supersymmetric matrix KP hierarchy and discuss the simplest examples.

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arXiv1997

Nonlinear realizations of superconformal and W algebras as embeddings of strings

We propose a simple method for constructing representations of (super)conformal and nonlinear W-type algebras in terms of their subalgebras and corresponding Nambu-Goldstone fields. We apply it to N=2 and N=1 superconformal algebras and describe in this way various embeddings of strings and superstrings for which these algebras and their subalgebras define world-sheet symmetries. Besides reproducing the known examples, we present some new ones, in particular an embedding of the bosonic string with additional U(1) affine symmetry into N=2 superstring. We also apply our method to the nonlinear $W_3^{(2)}$ algebra and demonstrate that the linearization procedure worked out for it some time ago gets a natural interpretation as a kind of string embedding. All these embeddings include the critical ones as particular cases.

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arXiv1997

Quantum N=2 super $W_3^{(2)}$ Algebra In Superspace

We discuss the N=2 extension of Polyakov-Bershadsky $W_3^{(2)}$ algebra with the generic central charge, $c$, at the quantum level in superspace. It contains, in addition to the spin 1 N=2 stress tensor, the spins $1/2, 2$ bosonic and spins $1/2, 2$ fermionic supercurrents satisfying the first class nonlinear chiral constraints. In the $c \to \infty $ limit, the ``classical'' N=2 $W_3^{(2)}$ algebra is recovered.

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arXiv1997

Hamiltonian structure and coset construction of the supersymmetric extensions of N=2 KdV hierarchy

A manifestly N=2 supersymmetric coset formalism is applied to analyse the "fermionic" extensions of N=2 $a=4$ and $a=-2$ KdV hierarchies. Both these hierarchies can be obtained from a manifest N=2 coset construction. This coset is defined as the quotient of some local but non-linear superalgebra by a $\hat{U(1)}$ subalgebra. Three superextensions of N=2 KdV hierarchy are proposed, among which one seems to be entirely new.

solv-int↗

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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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

The W(sl(N+3),sl(3)) algebras and their contractions to W3

We construct the nonlinear $W(sl(N+3),sl(3))$ algebras and find the spectrum of values of the central charge that gives rise, by contracting the $W(sl(N+3),sl(3))$ algebras, to a $W_3$ algebra belonging to the coset $W((sl(N+3),sl(3))/(u(1)\oplus sl(N))$. Part of the spectrum was conjectured before, but part of it is given here for the first time. Using the tool of embedding the $W(sl(N+3),sl(3))$ algebras into linearizing algebras, we construct new realizations of $W_3$ modulo null fields. The possibility to predict, within the conformal linearization framework, the central charge spectrum for minimal models of the nonlinear $W(sl(N+3),sl(3))$ algebras is discussed at the end.

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arXiv1996

Toward the construction of N=2 supersymmetric integrable hierarchies

We formulate a conjecture for the three different Lax operators that describe the bosonic sectors of the three possible $N=2$ supersymmetric integrable hierarchies with $N=2$ super $W_n$ second hamiltonian structure. We check this conjecture in the simplest cases, then we verify it in general in one of the three possible supersymmetric extensions. To this end we construct the $N=2$ supersymmetric extensions of the Generalized Non-Linear Schrödinger hierarchy by exhibiting the corresponding super Lax operator. To find the correct hamiltonians we are led to a new definition of super-residues for degenerate N=2 supersymmetric pseudodifferential operators. We have found a new non-polinomial Miura-like realization for $N=2$ superconformal algebra in terms of two bosonic chiral--anti--chiral free superfields.

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arXiv1995

Conformal Linearization Versus Nonlinearity of $W$-Algebras

We review the new approach to the theory of nonlinear $W$-algebras which is developed recently and called {\it conformal linearization}. In this approach $W$-algebras are embedded as subalgebras into some {\it linear conformal} algebras with a finite set of currents and most of their properties could be understood in a much simpler way by studing their linear counterpart. The general construction is illustrated by the examples of $u(N)$-superconformal, $W(sl(N),sl(2))$, $W(sl(N),sl(N))$ as well as $W(sl(N),sl(3))$ algebras. Applications to the construction of realizations (included modulo null fields realizations) as well as central charge spectrum for minimal models of nonlinear algebras are discussed. (To appear in ``Geometry and Integrable Models'', Eds.: P.N.Pyatov & S.N.Solodukhin, World Scientific Publ. Co. (in press)).

hep-th↗

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

Null Fields Realizations of $W_3$ from $W(sl(4),sl(3))$ and $W(sl(3|1),sl(3))$ Algebras

We consider the nonlinear algebras $W(sl(4),sl(3))$ and $W(sl(3|1),sl(3))$ and find their realizations in terms of currents spanning conformal linearizing algebras. The specific structure of these algebras, allows us to construct realizations modulo null fields of the $W_3$ algebra that lies in the cosets $W(sl(4),sl(3))/u(1)$ and $W(sl(3|1),sl(3))/u(1)$. Such realizations exist for the following values of the $W_3$ algebra central charge: $c_W=-30,-40/7,-98/5,-2$. The first two values are listed for the first time, whereas for the remaining values we get the new realizations in terms of an arbitrary stress tensor and $u(1)\times sl(2)$ affine currents.

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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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