<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> superconformal n-particle mechanics via superspace

Krivonos, S.; Lechtenfeld, Olaf; Polovnikov, Kirill

doi:10.1016/j.nuclphysb.2009.03.001

Cited by 31 publications

(49 citation statements)

References 24 publications

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“…to them). The WDVV equations appear also when constructing N = 4 supersymmetric/superconformal extensions of mechanics on n-dimensional Euclidean space (see [9,10,11,12,13,14] and refs. therein).…”

Section: Introductionmentioning

confidence: 99%

N=4 supersymmetric mechanics on curved spaces

Kozyrev¹,

Krivonos²,

Lechtenfeld

et al. 2018

Phys. Rev. D

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We present N ¼ 4 supersymmetric mechanics on n-dimensional Riemannian manifolds constructed within the Hamiltonian approach. The structure functions entering the supercharges and the Hamiltonian obey modified covariant constancy equations as well as modified Witten-Dijkgraaf-Verlinde-Verlinde equations specified by the presence of the manifold's curvature tensor. Solutions of original WittenDijkgraaf-Verlinde-Verlinde equations and related prepotentials defining N ¼ 4 superconformal mechanics in flat space can be lifted to soðnÞ-invariant Riemannian manifolds. For the Hamiltonian this lift generates an additional potential term which, on spheres and (two-sheeted) hyperboloids, becomes a Higgsoscillator potential. In particular, the sum of n copies of one-dimensional conformal mechanics results in a specific superintegrable deformation of the Higgs oscillator.

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Section: Introductionmentioning

confidence: 99%

N=4 supersymmetric mechanics on curved spaces

Kozyrev¹,

Krivonos²,

Lechtenfeld

et al. 2018

Phys. Rev. D

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“…It can be shown that it is just the definition of the metric that can be used to establish the relation between the superfield formalism and the curved WDVV equations. Let us use the idea of [13] and calculate the derivative of this metric:…”

Section: The Modified Metricmentioning

confidence: 99%

The curved WDVV equations and superfields

Kozyrev

2019

J. Phys.: Conf. Ser.

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We reproduce the N = 4 supersymmetric mechanics on curved spaces, constructed earlier within the Hamiltonian formalism, using the superfield methods. We show that for any such mechanics, given by the metric and the third order Codazzi tensor, it is possible to construct a suitable modification of irreducibility conditions of linear N = 4 multiplets and obtain the superfield Lagrangian by solving a simple differential equation. Also, we prove that the constructed irreducibility conditions are consistent if and only if the metric and Codazzi tensor satisfy the modification of the WDVV equations, which are the conditions of existence of N = 4 supersymmetry.

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“…The choice of OSp(4|2) is the unique one consistent with free kinetic terms for the bosonic fields, as long as one insists on the supercharges (4.30) being linear in fermionic variables [41]. Allowing for supercharge terms cubic in the fermionic operators will constrain their coefficient functions by the so-called WDVV equations [38,39,40,42,43,41]. It will be interesting to develop a superspace variant of this more general situation.…”

Section: Concluding Remarks and Outlookmentioning

confidence: 99%

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

Fedoruk¹,

Ivanov²,

Lechtenfeld

et al. 2018

J. High Energ. Phys.

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SU(2|1) supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an N = 4 supersymmetrization of the quantum U(2) spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra su(2|1). The full system admits an SU(2|1) covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum 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.2 It was shown in [17], that the centrally extended superalgebra su(2|1) can be represented as a semi-direct sum of su(2|1) and an extra R-symmetry generator: su(2|1) ≃ su(2|1)+ ⊃ u(1). The central charge is a combination of the R-symmetry generator and the internal U(1) generator of su(2|1). In the models under consideration the central charge operator is identified with the canonical Hamiltonian.3 The kinetic term of the variables Z k a in the action (1.5) is of the first-order in the time derivatives, in contrast to the dynamical variable X a b with the second-order kinetic term. Just for this reason we call Z k a ,Z a k semi-dynamical variables. In the Hamiltonian (see below), they appear only in the interaction terms and enter through the SU(2) current S (ik) .

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N=4 superconformal n-particle mechanics via superspace

Cited by 31 publications

References 24 publications

N=4 supersymmetric mechanics on curved spaces

N=4 supersymmetric mechanics on curved spaces

The curved WDVV equations and superfields

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

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