Papers by Sergey Krivonos
We obtain a uniform decomposition into Casimir eigenspaces (most of which are irreducible) of the... more We obtain a uniform decomposition into Casimir eigenspaces (most of which are irreducible) of the fourth power of the adjoint representation g ⊗4 for all simple Lie algebras. We present universal, in Vogel's sense, formulae for the dimensions and split Casimir operator's eigenvalues of all terms in this decomposition. We assume that a similar uniform decomposition into Casimir eigenspaces with universal dimension formulae exists for an arbitrary power of the adjoint representations.
Classical and Quantum Gravity, Sep 1, 1993
We extend the coset space formulation of the one-field realization of w 1+∞ to include more field... more We extend the coset space formulation of the one-field realization of w 1+∞ to include more fields as the coset parameters. This can be done either by choosing a smaller stability subalgebra in the nonlinear realization of w 1+∞ symmetry, or by considering a nonlinear realization of some extended symmetry, or by combining both options. We show that all these possibilities give rise to the multi-field realizations of w 1+∞. We deduce the twofield realization of w 1+∞ proceeding from a coset space of the symmetry groupG which is an extension of w 1+∞ by the second self-commuting set of higher spin currents. Next, starting with the unextended w 1+∞ but placing all its spin 2 generators into the coset, we obtain a new two-field realization of w 1+∞ which essentially involves a 2D dilaton. In order to construct the invariant action for this system we add one more field and so get a new three-field realization of w 1+∞. We re-derive it within the coset space approach, by applying the latter to an extended symmetry groupĜ which is a nonlinear deformation ofG. Finally we present some multi-field generalizations of our three-field realization and discuss several intriguing parallels with N = 2 strings and conformal affine Toda theories.
arXiv (Cornell University), Dec 30, 2022
We constructed characteristic identities for the 3-split (polarized) Casimir operators of simple ... more We constructed characteristic identities for the 3-split (polarized) Casimir operators of simple Lie algebras in the adjoint representations ad and deduced a certain class of subrepresentations in ad ⊗3. The projectors onto invariant subspaces for these subrepresentations were directly constructed from the characteristic identities for the 3-split Casimir operators. For all simple Lie algebras, universal expressions for the traces of higher powers of the 3-split Casimir operators were found and dimensions of the subrepresentations in ad ⊗3 were calculated. All our formulas are in agreement with the universal description of (irreducible) subrepresentations in ad ⊗3 for simple Lie algebras in terms of the Vogel parameters.
SSRN Electronic Journal
Recently A.Galajinsky has suggested the N = 1 supersymmetric extension of Euler top and made a fe... more Recently A.Galajinsky has suggested the N = 1 supersymmetric extension of Euler top and made a few interesting observations on its properties [1]. In this paper we use the formulation of the Euler top as a system on complex projective plane, playing the role of phase space, i.e. as a onedimensional mechanical system. Then we suggest the supersymmetrization scheme of the generic one-dimensional systems with positive Hamiltonian which yieldsá priori integrable family of N = 2k supersymmetric Hamiltonians parameterized by N /2 arbitrary real functions.
Journal of Physics: Conference Series, 2019
In this notes, we derive the component on-shell action of the space-filling D2-brane, i.e. N = 1,... more In this notes, we derive the component on-shell action of the space-filling D2-brane, i.e. N = 1, d = 3 supersymmetric Born-Infeld action within the nonlinear realization approach. The Bianchi identity admits direct covariantization with respect to the broken N = 1, d = 3 supersymmetry. In the corresponding on-shell component action all fermionic terms combine into covariant, with respect to broken supersymmetry, objects: covariant derivatives and fierbein and therefore the D2-brane component action has very simple form. Similarly to the cases of p-branes, it mimics the bosonic Born-Infeld action.
Physical Review D
In this paper we demonstrate that the different generalizations of the Schwarzians, supersymmetri... more In this paper we demonstrate that the different generalizations of the Schwarzians, supersymmetric or purely bosonic, can be easily constructed by using the nonlinear realizations technique.
Physical Review, Oct 29, 2006
We construct the general action for $N=4, d=1$ nonlinear supermultiplet including the most genera... more We construct the general action for $N=4, d=1$ nonlinear supermultiplet including the most general interaction terms which depend on the arbitrary function $h$ obeying the Laplace equation on $S^3$. We find the bosonic field $B$ which depends on the components of nonlinear supermultiplet and transforms as a full time derivative under N=4 supersymmetry. The most general interaction is generated just by a Fayet-Iliopoulos term built from this auxiliary component. Being transformed through a full time derivative under $N=4, d=1$ supersymmetry, this auxiliary component $B$ may be dualized into a fourth scalar field giving rise to a four dimensional $N=4, d=1$ sigma-model. We analyzed the geometry in the bosonic sector and find that it is not a hyper-Kahler one. With a particular choice of the target space metric $g$ the geometry in the bosonic sector coincides with the one which appears in heterotic $(4,0)$ sigma-model in $d=2$
Physics Letters B
We analyze the integrability of the N-extended supersymmetric Calogero-Moser model. We explicitly... more We analyze the integrability of the N-extended supersymmetric Calogero-Moser model. We explicitly construct the Lax pair {L, A} for this system, which properly reproduces all equations of motion. After adding a supersymmetric oscillator potential we reduce the latter to solvingU = A U for the time evolution operator U(t). The bosonic variables, however, evolve independently of U on closed trajectories, as is required for superintegrability. To visualize the structure of the conserved currents we derive the complete set of Liouville charges up to the fifth power in the momenta, for the N = 2 supersymmetric model. The additional, non-involutive, conserved charges needed for a maximal superintegrability of this model are also found.
It was recently demonstrated that super-Schwarzian derivatives can be constructed from the Cartan... more It was recently demonstrated that super-Schwarzian derivatives can be constructed from the Cartan forms of the super-conformal supergroups OSp(1|2), SU(1, 1|1), OSp(3|2), SU(1, 1|2). Roughly speaking, the superSchwarzian is just the component of the corresponding Cartan forms with the lowest dimension. In this paper, we apply the same approach for superalgebra D(1, 2;α). The minimal set of constraints we used includes: a) introducing new superspace coordinates the Cartan forms depend on, which are completely invariant with respect to the corresponding group; b) nullifying the form for dilatation. In contrast to the SU(1, 1|2) case, the new super-Schwarzian appears to be a dθ component of the form for su(2) automorphism. PACS numbers: 11.30.Pb, 11.30.-j
In this paper we revisit the construction of supersymmetric Schwarzians using nonlinear realizati... more In this paper we revisit the construction of supersymmetric Schwarzians using nonlinear realizations. We show that N = 0, 1, 2, 3, 4 supersymmetric Schwarzians can be systematically obtained as certain projections of Maurer-Cartan forms of superconformal groups after imposing simple conditions on them. We also present the supersymmetric Schwarzian actions defined as the integrals of products of Cartan forms. In contrast with the previous attempts to obtain the super-Schwarzians within nonlinear realizations technique, our set of constraints does not impose any restriction on the super-Schwarzians. PACS numbers: 11.30.Pb, 11.30.-j
Starting from the Hamiltonian formulation of supersymmetric Calogero models associated with the c... more Starting from the Hamiltonian formulation of supersymmetric Calogero models associated with the classical A_n, B_n, C_n and D_n series we construct the N= 2 and N= 4 supersymmetric extensions of the their hyperbolic/trigonometric Calogero-Sutherland cousins. The bosonic core of these models are the standard Calogero-Sutherland hyperbolic/trigonometric systems.
Nonlinear realizations superfield techniques, pertinent to the description of partial breaking of... more Nonlinear realizations superfield techniques, pertinent to the description of partial breaking of global N=2 supersymmetry in a flat d=4 super Minkowski background, are generalized to the case of partially broken N=1 AdS5 supersymmetry SU(2,2|1). We present, in an explicit form, off-shell manifestly N=1, d=4 supersymmetric minimal Goldstone superfield actions for two patterns of partial breaking of SU(2,2|1) supersymmetry. They correspond to two different nonlinear realizations of the latter, in the supercosets with the AdS5 and AdS5\times S1 bosonic parts. The relevant worldvolume Goldstone supermultiplets are accommodated, respectively, by improved tensor and chiral N=1, d=4 superfields. The second action is obtained from the first one by dualizing the improved tensor Goldstone multiplet into a chiral Goldstone one. In the bosonic sectors, the first and second actions yield static-gauge Nambu-Goto actions for a L3-brane on AdS5 and a scalar 3-brane on AdS5\times S1.
Based on the concept of the partial breaking of global supersymmetry (PBGS), we derive the worldv... more Based on the concept of the partial breaking of global supersymmetry (PBGS), we derive the worldvolume superfield equations of motion for N=1, D=4 supermembrane, as well as for the space-time filling D2- and D3-branes, from nonlinear realizations of the corresponding supersymmetries. We argue that it is of no need to take care of the relevant automorphism groups when being interested in the dynamical equations. This essentially facilitates computations. As a by-product, we obtain a new polynomial representation for the d=3,4 Born-Infeld equations, with merely a cubic nonlinearity.
We find, at the Lagrangian off-shell level, the explicit equivalence transformation which relates... more We find, at the Lagrangian off-shell level, the explicit equivalence transformation which relates the conformal mechanics of De Alfaro, Fubini and Furlan to the conformal mechanics describing the radial motion of the charged massive particle in the Bertotti-Robinson AdS_2× S^2 background. Thus we demonstrate the classical equivalence of these two systems which are usually regarded as essentially different "old" and "new" conformal mechanics models. We also construct a similar transformation for N=2, SU(1,1|1) superconformal mechanics in N=2 superfield formulation. Performing this transformation in the action of the N=2 superconformal mechanics, we find an off-shell superfield action of N=2 superextension of Bertotti-Robinson particle. Such an action has not been given before. We show its on-shell equivalence to the AdS_2 superparticle action derived from the spontaneous partial breaking of SU(1,1|1) superconformal symmetry treated as the N=2 AdS_2 supersymmetry.
Proceeding from the superfield action for N=4, d=1 nonlinear supermultiplet, equipped with the mo... more Proceeding from the superfield action for N=4, d=1 nonlinear supermultiplet, equipped with the most general potential term, we find the action describing a charged particle on the sphere S^3 in the field of n fixed Dirac dyons. We construct the supercharges and Hamiltonian and analyze some particulary interesting potentials corresponding to the N=4 supersymmetric extension of the integrable one- and two-center McIntosh--Cisneros--Zwanziger--Kepler (MICZ-Kepler) systems on S^3.
We present the minimal realization of the ℓ-conformal Galilei group in 2+1 dimensions on a single... more We present the minimal realization of the ℓ-conformal Galilei group in 2+1 dimensions on a single complex field. The simplest Lagrangians yield the complex Pais-Uhlenbeck oscillator equations. We introduce a minimal deformation of the ℓ=1/2 conformal Galilei (a.k.a. Schrödinger) algebra and construct the corresponding invariant actions. Based on a new realization of the d=1 conformal group, we find a massive extension of the near-horizon Kerr-dS/AdS metric.
We explicitly construct a supersymmetric so(n) spin-Calogero model with an arbitrary even number ... more We explicitly construct a supersymmetric so(n) spin-Calogero model with an arbitrary even number N of supersymmetries. It features 1/2 Nn(n+1) rather than Nn fermionic coordinates and a very simple structure of the supercharges and the Hamiltonian. The latter, together with additional conserved currents, form an osp( N|2) superalgebra. We provide a superspace description for the simplest case, namely N=2 supersymmetry. The reduction to an N-extended supersymmetric goldfish model is also discussed.
We propose a new reduction mechanism which allows one to construct n-particle (super)conformal th... more We propose a new reduction mechanism which allows one to construct n-particle (super)conformal theories with pairwise interaction starting from a composite system involving n(n-1)/2+1 copies of the ordinary (super)conformal mechanics. Applications of the scheme include an N=4 superconformal extension for a complexification of the Calogero model and a D(2,1|\alpha)-invariant n-particle system.
The integrable close and open chain models can be formulated in terms of generators of the Hecke ... more The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe vectors for two--component and inhomogeneous models. We also find the Bethe vectors for the fermionic realization of the integrable XXX and XXZ close chain models by means of the algebraic and coordinate Bethe ansatz. Special modification of the XXZ closed spin chain model ("small polaron model") is consedered. Finally, we discuss some questions relating to the general open Hecke chain models.
Proceeding from nonlinear realizations of the most general N=4, d=1 superconformal symmetry assoc... more Proceeding from nonlinear realizations of the most general N=4, d=1 superconformal symmetry associated with the supergroup D(2,1;\alpha), we construct all known and two new off-shell N=4, d=1 supermultiplets as properly constrained N=4 superfields. We find plenty of nonlinear interrelations between the multiplets constructed and present a few examples of invariant superfield actions for them. The superconformal transformation properties of these multiplets are explicit within our method.
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Papers by Sergey Krivonos