Searcharxiv⌕ Search

arXiv subjects

Sergey Fedoruk

Publications and source records attributed to Sergey Fedoruk.

At least 19 recordsLinked to original sources
arXiv2026

${\cal N}{=}\,4$ supersymmetric multiparticle systems based on indecomposable multiplets

We construct new multiparticle models of $\mathcal{N}=4$ supersymmetric mechanics with spin degrees of freedom by employing nonlinear indecomposable supermultiplets ${\bf (1,4,3){\supset\hspace{-1.1em}+}(4,4,0)}$. These systems are proper deformations of those associated with the standard irreducible $d=1$, $\mathcal{N}=4$ multiplets. In this way we find a deformation of $\mathcal{N}=4$ supersymmetric U$(2)$-spin rational Calogero system invariant under $d=1$ superconformal group OSp$(4|2)$. One more deformed model reproduces $\mathcal{N}=4$ supersymmetric U$(2)$-spin hyperbolic Calogero system, up to a shift of the Hamiltonian by some U$(1)$ generators.

hep-th↗
arXiv2024

$\mathcal{N}{=}\,8$ invariant interaction of dynamical and semi-dynamical $\mathcal{N}{=}\,4$ multiplets

We present a new model of $\mathcal{N}{=}\,8$ mechanics with semi-dynamic supermultiplets. The model is constructed as an interaction of $\mathcal{N}{=}\,4$ supermultiplets which carry an implicit $\mathcal{N}{=}\,4$ supersymmetry. The initial field content consists of three dynamical $({\bf 1, 4, 3})$ multiplets: one bosonic and two fermionic. To ensure implicit $\mathcal{N}{=}\,4$ supersymmetry, we introduce the superfields describing three semi-dynamical $({\bf 4, 4, 0})$ multiplets: one fermionic and two bosonic. To avoid the second-order Lagrangian for fermions from the fermionic $({\bf 1, 4, 3})$ multiplets, the conversion of their velocities into new auxiliary fields is carried out. After conversion, these multiplets turn into semi-dynamical mirror $({\bf 4, 4, 0})$ multiplets without non-canonical terms in the $\mathcal{N}{=}\,8$ Lagrangian at the component level. The final $\mathcal{N}{=}\,8$ multiplet content is $({\bf 1, 8, 7}) \oplus ({\bf 8, 8, 0})$. As a first step to the ultimate $\mathcal{N}{=}\,4$ superfield formulation of the model, we remind a natural description of the standard and mirror $({\bf 4, 4, 0})$ multiplets in the framework of $\mathcal{N}{=}\,4, d{=}\,1$ biharmonic superspace.

hep-th↗
arXiv2022

Supersymmetrization of the 3-particle elliptic Calogero model

$\mathcal{N}{=}\,2$ and $\mathcal{N}{=}\,4$ supersymmetric generalizations of the 3-particle elliptic Calogero system are proposed. Supersymmetry generators of the system are found in which the center of mass sector is described by the supermultiplet ${\bf (1,\mathcal{N},\mathcal{N}-1)}$, while the sector of relative coordinates is the supermultiplet ${\bf (2,\mathcal{N},\mathcal{N}- 2)}$. The $\mathcal{N}{=}\,2$ model described with three supermultiplets ${\bf (1,2,1)}$ is also presented.

hep-th↗
arXiv2022

Relativistic generalization of the rational Calogero model

A relativistic generalization of the rational Calogero model is obtained by using the deformation of a gauging matrix system with extra semi-dynamical variables. The Hamiltonian of this system is derived by imposing the gauge fixing conditions and eliminating gauge degrees of freedom. The integrability of the proposed relativistic model is proved.

hep-th↗
arXiv2020

$\mathcal{N}{=}\,4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model

The $\mathcal{N}{=}\,4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model with odd matrix fields is examined. Explicit form of the $\mathcal{N}{=}\,4$ supersymmetry generators is derived. The Lax representation for the dynamics of the $\mathcal{N}{=}\,4$ hyperbolic $\mathrm{U}(2)$-spin Calogero-Sutherland system is found. The reduction to the $\mathcal{N}{=}\,4$ supersymmetric spinless hyperbolic Calogero-Sutherland system is established.

hep-th↗
arXiv2020

$\mathcal{N}{=}\,2$ supersymmetric hyperbolic Calogero-Sutherland model

The $\mathcal{N}{=}\,2$ supersymmetric hyperbolic Calogero-Sutherland model obtained in arXiv:1902.08023 by gauging the $\mathcal{N}{=}\,2$ superfield matrix system is studied. Classical and quantum $\mathcal{N}{=}\,2$ supersymmetry generators are found. The difference in the structure of classical and quantum supercharges is established. It is shown that, unlike classical supercharges, quantum supersymmetry generators can be limited to an invariant sub-sector that does not contain off-diagonal fermion operators. The Lax pair for supersymmetric generalization of the hyperbolic Calogero-Sutherland system is constructed.

hep-th↗
arXiv2019

Supersymmetric hyperbolic Calogero-Sutherland models by gauging

Novel $\mathcal{N}{=}\,2$ and $\mathcal{N}{=}\,4$ supersymmetric extensions of the Calogero-Sutherland hyperbolic systems are obtained by gauging the ${\rm U}(n)$ isometry of matrix superfield models. The bosonic core of the $\mathcal{N}{=}\,2$ models is the standard $A_{n-1}$ Calogero-Sutherland hyperbolic system, whereas the ${\mathcal N}{=}\,4$ model contains additional semi-dynamical spin variables and is an extension of the U(2) spin Calogero-Sutherland hyperbolic system. We construct two different versions of the ${\mathcal N}{=}\,4$ model, with and without the interacting center-of-mass coordinate in the bosonic sector.

hep-th↗
arXiv2018

Multiparticle $\mathcal{N}{=}\,8$ mechanics with $F(4)$ superconformal symmetry

We present a new multiparticle model of $\mathcal{N}{=}\,8$ mechanics with superconformal $F(4)$ symmetry. The system is constructed in terms of two matrix $\mathcal{N}{=}\,4$ multiplets. One of them is a bosonic matrix $({\bf 1, 4, 3})$ multiplet and another is a fermionic $({\bf 0, 4, 4})$ one. Off-diagonal bosonic components of the $({\bf 1, 4, 3})$ multiplet are chosen to take values in the flag manifold $\mathrm{U}(n)/[\mathrm{U}(1)]^n$ and they carry additional gauge symmetries. The explicit form of the $F(4)$ supersymmetry generators is found. We demonstrate that the $F(4)$ superalgebra constructed contains as subalgebras two different $D(2,1;α\,{=}{-}1/3)$ superalgebras intersecting over the common $sl(2,\mathbb{R})\oplus su(2)$ subalgebra.

hep-th↗
arXiv2018

Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems

${\rm SU}(2|1)$ supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an $\mathcal{N}{=}\,4$ supersymmetrization of the quantum ${\rm U}(2)$ spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra $\widehat{su}(2|1)$. The full system admits an ${\rm SU}(2|1)$ covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum ${\rm SU}(2|1)$ generators in both sectors as well as for the total system, and we determine the relevant energy spectra, degeneracies, and the sets of physical states.

hep-th↗
arXiv2018

From $\mathcal{N}{=}\,4$ Galilean superparticle to three-dimensional non-relativistic $\mathcal{N}{=}\,4$ superfields

We consider the general $\mathcal{N}{=}\,4,$ $d{=}\,3$ Galilean superalgebra with arbitrary central charges and study its dynamical realizations. Using the nonlinear realization techniques, we introduce a class of actions for $\mathcal{N}{=}\,4$ three-dimensional non-relativistic superparticle, such that they are linear in the central charge Maurer-Cartan one-forms. As a prerequisite to the quantization, we analyze the phase space constraints structure of our model for various choices of the central charges. The first class constraints generate gauge transformations, involving fermionic $κ$-gauge transformations. The quantization of the model gives rise to the collection of free $\mathcal{N}{=}\,4$, $d{=}\,3$ Galilean superfields, which can be further employed, e.g., for description of three-dimensional non-relativistic $\mathcal{N}{=}\,4$ supersymmetric theories.

hep-th↗
arXiv2018

Deformed supersymmetric quantum mechanics with spin variables

We quantize the one-particle model of the ${\rm SU}(2|1)$ supersymmetric multi-particle mechanics with the additional semi-dynamical spin degrees of freedom. We find the relevant energy spectrum and the full set of physical states as functions of the mass-dimension deformation parameter $m$ and ${\rm SU}(2)$ spin $q \in \big( \mathbb{Z}_{>0}\,$, $1/2 + \mathbb{Z}_{\geqslant 0}\big)\,$. It is found that the states at the fixed energy level form irreducible multiplets of the supergroup ${\rm SU}(2|1)\,$. Also, the hidden superconformal symmetry ${\rm OSp}(4|2)$ of the model is revealed in the classical and quantum cases. We calculate the ${\rm OSp}(4|2)$ Casimir operators and demonstrate that the full set of the physical states belonging to different energy levels at fixed $q$ are unified into an irreducible ${\rm OSp}(4|2)$ multiplet.

hep-th↗
arXiv2016

Gauged spinning models with deformed supersymmetry

New models of the SU(2|1) supersymmetric mechanics based on gauging the systems with dynamical (1,4,3) and semi-dynamical (4,4,0) supermultiplets are presented. We propose a new version of SU(2|1) harmonic superspace approach which makes it possible to construct the Wess-Zumino term for interacting (4,4,0) multiplets. A new N=4 extension of d=1 Calogero-Moser multiparticle system is obtained by gauging the U(n) isometry of matrix SU(2|1) harmonic superfield model.

hep-th↗
arXiv2015

Comments on HKT supersymmetric sigma models and their Hamiltonian reduction

Using complex notation, we present new simple expressions for two pairs of complex supercharges in HKT supersymmetric sigma models. The second pair of supercharges depends on the holomorphic antisymmetric "hypercomplex structure" tensor which plays the same role for the HKT models as the complex structure tensor for the Kaehler models. When the Hamiltonian and supercharges commute with the momenta conjugate to the imaginary parts of the complex coordinates, one can perform a Hamiltonian reduction. The models thus obtained represent a special class of quasicomplex sigma models introduced recently by Ivanov and Smilga.

hep-th↗
arXiv2014

Massive twistor particle with spin generated by Souriau-Wess-Zumino term and its quantization

We present new model of D=4 relativistic massive particle with spin and we describe its quantization. The model is obtained by an extension of standard relativistic phase space description of massive spinless particle by adding new topological Souriau-Wess-Zumino term which depends on spin fourvector variable. We describe equivalently our model as given by the free two-twistor action with suitable constraints. An important tool in our derivation is the spin-dependent twistor shift, which modifies standard Penrose incidence relations. The quantization of the model provides the wave function with correct mass and spin eigenvalues.

hep-th↗
arXiv2013

N=4 mechanics with diverse (4,4,0) multiplets: explicit examples of HKT, CKT, and OKT geometries

We present simple models of N=4 supersymmetric mechanics with ordinary and mirror linear (4,4,0) multiplets that give a transparent description of HKT, CKT, and OKT geometries. These models are treated in the N=4 and N=2 superfield approaches, as well as in the component approach. Our study makes manifest that the CKT and OKT supersymmetric sigma models are distinguished from the more simple HKT models by the presence of extra holomorphic torsions in the supercharges.

hep-th↗
arXiv2013

Maxwell group and HS field theory

We consider the master fields for HS multiplets defined on 10-dimensional tensorial extension \tilde{\cal M} of D=4 space-time described as a coset \tilde{\cal M}={\cal M}/Sl(2;C) of 16-parameter Maxwell group {\cal M}. The tensorial coordinates provide a geometrization of the coupling to constant uniform EM fields. We describe the spinorial model in extended space-time \tilde{\cal M} and by its first quantization we obtain new infinite HS-Maxwell multiplets with their massless components coupled to each other through constant EM background. We conclude our report by observing that three-dimensional spinorial model with a pair of spinors should provide after quantization D=3 massive HS-Maxwell multiplets.

hep-th↗
arXiv2013

New spinorial particle model in tensorial space-time and interacting higher spin fields

The Maxwell-covariant particle model is formulated in tensorial extended D=4 space-time (x_mu, z_{mu nu}) parametrized by ten-dimensional coset of D=4 Maxwell group, with added auxiliary Weyl spinors lambda_alpha, y^alpha. We provide the Hamiltonian quantization of the model and demonstrate that first class constraints modify the known equations obtained for massless higher spin fields in flat tensorial space-time. We obtain the Maxwell-covariant field equations for new infinite dimensional spin multiplets. The component fields assigned to different spin values are linked by couplings proportional to rescaled electromagnetic coupling constant \tilde e = em, where m is the mass-like parameter introduced in our model. We discuss briefly the geometry of our tensorial space-time with constant torsion and its relation with the presence of constant electromagnetic background.

hep-th↗