6 research outputs found
Extended supersymmetric multiparticle Euler-Calogero-Moser model
We review the construction of supersymmetric extension of the n-particle Euler-Calogero-Moser model within the Hamiltonian approach [1]. The main feature of the proposed supersymmetrization method is that it is automatically adapted for a model with an arbitrary even number of supersymmetries. It is shown that the number of fermions that must be used in this construction is 1/2N n(n+1). We demonstrate that the resulting supersymmetric system is dynamically invariant with respect to the superconformal group and give the explicit realization of its generators in terms of the conserved currents. For the simplest case of the supersymmetric n-particle Euler-Calogero-Moser model we provide its description in superspace by using the corresponding constrained superfields. © 2019 Published under licence by IOP Publishing Ltd
N=4 Supersymmetry and the BPST Instanton
In this paper we construct the Lagrangian and Hamiltonian formulations of N=4
supersymmetric systems describing the motion of an isospin particle on a
conformally flat four-manifold with SO(4) isometry carrying the non-Abelian
field of a BPST instanton. The conformal factor can be specified to yield
various particular systems, such as superconformally invariant mechanics as
well as a particle on the four-sphere, the pseudosphere or on R x S^3. The
isospin degrees of freedom arise as bosonic components of an additional
fermionic N=4 supermultiplet, whose other components are rendered auxiliary by
a nonlocal redefinition. Our on-shell component action coincides with the one
recently proposed in arXiv:0912.3289.Comment: 1+8 pages; v2: two references added, published versio
Dynamical supersymmetry of spin particle-magnetic field interaction
We study the super and dynamical symmetries of a fermion in a monopole
background. The Hamiltonian also involves an additional spin-orbit coupling
term, which is parameterized by the gyromagnetic ratio. We construct the
superinvariants associated with the system using a SUSY extension of a
previously proposed algorithm, based on Grassmann-valued Killing tensors.
Conserved quantities arise for certain definite values of the gyromagnetic
factor: SUSY requires ; a Kepler-type dynamical symmetry only
arises, however, for the anomalous values and . The two anomalous
systems can be unified into an SUSY system built by doubling the number
of Grassmann variables. The planar system also exhibits an supersymmetry
without Grassmann variable doubling.Comment: 23 page
Superconformal mechanics
We survey the salient features and problems of conformal and superconformal
mechanics and portray some of its developments over the past decade. Both
classical and quantum issues of single- and multiparticle systems are covered.Comment: 1+68 pages, invited review for Journal of Physics A; v2: revised text
extended by 4 pages and 11 references, published versio
Curved WDVV equation and supersymmetric mechanics
We extend the relation between the Witten-Dijkgraaf-Verlinde-Verlinde equation and N = 4 supersymmetric mechanics to arbitrary curved spaces. The resulting curved WDVV equation is written in terms of the third rank Codazzi tensor. We provide the solutions of the curved WDVV equation for the so(n) symmetric conformally flat metrics. We also explicitly demonstrate how each solution of the flat WDVV equation can be lifted up to the curved WDVV solution on the conformally flat spaces. © Published under licence by IOP Publishing Ltd