arXiv subjects

Sergey Krivonos

Publications and source records attributed to Sergey Krivonos.

At least 19 recordsLinked to original sources

arXiv2025

New variants of $N=3,4$ superconformal mechanics

We construct superconformal mechanics with $N=3$ and $N=4$ supersymmetries that were inspired by analogies with the supersymmetric Schwarzian mechanics. The Schwarzian, being another system with superconformal symmetry, provides insight into the field content of supersymmetric mechanics, most notably, on the number and properties of the fermionic fields involved. Adding more fermionic fields (four in the $N=3$ case and eight in the $N=4$ case) made it possible to construct systems possessing maximal superconformal symmetries in $N=3$ and $N=4$, namely $OSp(3|2)$ and $D(1,2;α)$. In the case of $N=4$ supersymmetry, we explicitly construct a new variant of $N=4$ superconformal mechanics in which all bosonic subalgebras of $D(1,2;α)$ superalgebra have bosonic realization. In addition, the constructed systems involve $so(3)$ currents whose parametrization is not fixed, which allows to consider different underlying geometries.

hep-th↗

arXiv2025

Two faces of $N=7,8$ superconformal mechanics

Two variants of $N=7$ superconformal mechanics with manifest $so(7)$ and $su(2) \times su(2)$ $R$-symmetries possessing exceptional $G(3)$ dynamical symmetry are presented. To construct these $G(3)$ theories, we developed two new versions of covariant embedding of the exceptional $g_2$ algebra into the $so(7)$ algebra and then the embedding of $so(7)$ into $so(8)$. As a result, two $N=8$ superconformal mechanics with the $OSp(8|2)$ and $F(4)$ superconformal algebras and $N=7, G(3)$ superconformal mechanics were constructed in a uniform way. The constants of the octonion multiplication play a key role in the construction of superconformal mechanics with manifest $so(7)$ symmetry.

hep-th↗

arXiv2025

Note on supersymmetric mechanics with spin-orbit interaction

We propose a simple model of two-dimensional N=2 superconformal mechanics with a spin-orbit interaction term and demonstrate that it inherits the Galilean symmetry of the initial free-particle system. We then propose a quaternionic counterpart of this system, which describes the four-dimensional N=4 superconformal mechanics$D(1,2|\alpha). The bosonic part of the Hamiltonian describes a free particle on the cone, while the fermionic part necessarily includes the spin-orbit interaction term.

hep-th↗

arXiv2025

N=8 superconformal mechanics: direct construction

In the present paper we constructed the supercharges and Hamiltonians for all variants of superconformal mechanics associated with the superalgebras $osp(8|2), {\mathfrak F(4)}, osp(4^\star |4)$, and $su(1,1|4)$. The fermionic and bosonic fields involved were arranged into generators spanning $so(8), so(7), so(5)\oplus su(2)$ and $su(4) \oplus u(1)$ $R$-symmetry currents of the corresponding superconformal algebras. The bosonic and fermionic parts of these $R$-symmetry generators separately define the constants of motion and form the same algebras. The angular part of the supercharges defining the system have the structure ``$(R-symmetry\; generators)\, \times\, fermions$'' while the angular part of Hamiltonian is just a proper sum of full Casimir operators and its purely bosonic and fermionic parts. We also constructed the explicit embedding of the algebras $so(7), \, so(5) \times su(2)$, and $su(4)\times u(1)$ into $so(8)$, which provide the possibility to explicitly construct the corresponding supercharges.

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arXiv2024

Note on $\mathcal{N}=8$ supersymmetric mechanics with dynamical and semi-dynamical multiplets

We give a Hamiltonian formulation of the new model of $\mathcal{N}=8$ supersymmetric mechanics recently proposed by S.~Fedoruk and E.~Ivanov and show that it possesses the dynamical $\mathcal{N}=8$ superconformal symmetry $osp(8|2)$. The bosonic part of the Hamiltonian is just a free particle on eight-dimensional cone embedded in nine-dimensional pseudo-Euclidean space, while the fermionic part can be interpreted as a spin-orbit interaction term.

hep-th↗

arXiv2024

On the origin of Higher Schwarzians

In this paper, we analyze higher Schwarzians and show that they are closely related to the nonlinear realization of the Virasoro algebra. The Goldstone fields of such a realization provide a new set of SL(2,R) invariant higher Schwarzians that are deeply related to the Aharonov,Tamanoi and Bonora-Matone ones. A minor change of the coset space parametrization leads to a new set of SL(2,R) non-invariant higher Schwarzians now related to the Schippers and Bertilsson Schwarzians.

hep-th↗

arXiv2024

The uniform structure of $\mathfrak{g}^{\otimes 4}$

We obtain a uniform decomposition into Casimir eigenspaces (most of which are irreducible) of the fourth power of the adjoint representation $\mathfrak{g}^{\otimes 4}$ 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.

math-ph↗

arXiv2022

Generalized Schwarzians

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.

hep-th↗

arXiv2022

Integrability of supersymmetric Calogero-Moser models

We analyze the integrability of the ${\cal N}$-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 solving $\dot{U}\,{=}\,A\,U$ 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 ${\cal N}{=}\,2$ supersymmetric model. The additional, non-involutive, conserved charges needed for a maximal superintegrability of this model are also found.

hep-th↗

arXiv2022

Euler top and freedom in supersymmetrization of one-dimensional mechanics

Recently A.Galajinsky has suggested the N=1 supersymmetric extension of Euler top and made a few interesting observations on its properties [arXiv:2111.06083 [hep-th]]. 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 one-dimensional mechanical system. Then we suggest the supersymmetrization scheme of the generic one-dimensional systems with positive Hamiltonian which yields a priori integrable family of N=2k supersymmetric Hamiltonians parameterized by N/2 arbitrary real functions.

hep-th↗

arXiv2022

(super)Schwarzian mechanics

In this paper we revisit the construction of supersymmetric Schwarzians using nonlinear realizations. We show that ${\cal N}=0,1,2,3,4$ 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.

hep-th↗

arXiv2022

${\cal N}{=}4$ supersymmetric Schwarzian with $D(1,2;α)$ symmetry

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 super-Schwarzian 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 $dθ^{ia}$ component of the form for $su(2)$ automorphism.

hep-th↗

arXiv2021

Kähler geometry for $su(1,N|M)$-superconformal mechanics

We suggest the $su(1,N|M)$-superconformal mechanics formulated in terms of phase superspace given by the non-compact analogue of complex projective superspace $\mathbb{CP}^{N|M}$. We parameterized this phase space by the specific coordinates allowing to interpret it as a higher-dimensional super-analogue of the Lobachevsky plane parameterized by lower half-plane (Klein model). Then we introduced the canonical coordinates corresponding to the known separation of the "radial" and "angular" parts of (super)conformal mechanics. Relating the "angular" coordinates with action-angle variables we demonstrated that proposed scheme allows to construct the $su(1,N|M)$ supeconformal extensions of wide class of superintegrable systems. We also proposed the superintegrable oscillator- and Coulomb- like systems with a $su(1,N|M)$ dynamical superalgebra, and found that oscillator-like systems admit deformed $\mathcal{N}=2M$ Poincaré supersymmetry, in contrast with Coulomb-like ones.

hep-th↗

arXiv2021

New approach to ${\cal N} {=}2$ supersymmetric Ruijsenaars-Schneider model

We present a very simple form of the supercharges and the Hamiltonian of ${\cal N} {=}\,2$ supersymmetric extension of $n$-particle Ruijsenaars--Schneider models for three cases of the interaction: $1/(x_i-x_j)$, $1/tan(x_i-x_j)$, $1/tanh(x_i-x_j)$. The long "fermionic tails" of the supercharges and Hamiltonian rolled up in the simple rational functions depending on fermionic bilinears.

hep-th↗

arXiv2020

N=4 super-Schwarzian via nonlinear realizations

Current studies of supersymmetric extensions of the Sachdev-Ye-Kitaev model stimulate a renewed interest in super-Schwarzian derivatives. In this work, we apply the method of nonlinear realizations to the finite-dimensional superconformal group SU(1,1|2) and link its invariants to the N=4 super-Schwarzian.

hep-th↗

arXiv2020

On ${\cal N}{=}\,2$ supersymmetric Ruijsenaars-Schneider models

We construct an ${\cal N}{=}\,2$ supersymmetric extension of $n$-particle Ruijsenaars-Schneider models. The guiding feature is a deformation of the phase space. The supercharges have a "free" form linear in the fermions but produce an interacting four-fermion Hamiltonian. A field-dependent unitary transformation maps to standard fermions obeying conventional Poisson brackets. In this frame, the supercharges and Hamiltonian have long "fermionic tails". We also comment on previous attempts in this direction.

hep-th↗

arXiv2020

New ${\cal N}{=}\,2$ superspace Calogero models

Starting from the Hamiltonian formulation of ${\cal N}{=}\,2$ supersymmetric Calogero models associated with the classical $A_n, B_n, C_n$ and $D_n$ series and their hyperbolic/trigonometric cousins, we provide their superspace description. The key ingredients include $n$ bosonic and $2n(n{-}1)$ fermionic ${\cal N}{=}\,2$ superfields, the latter being subject to a nonlinear chirality constraint. This constraint has a universal form valid for all Calogero models. With its help we find more general supercharges (and a superspace Lagrangian), which provide the ${\cal N}{=}\,2$ supersymmetrization for bosonic potentials with arbitrary repulsive two-body interactions.

hep-th↗

arXiv2020

${\cal N}{=}\,4$ supersymmetric Calogero-Sutherland models

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 ${\cal N}{=}\,2$ and ${\cal N}{=}\,4$ supersymmetric extensions of the their hyperbolic/trigonometric Calogero-Sutherland cousins. The bosonic core of these models are the standard Calogero-Sutherland hyperbolic/trigonometric systems.

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