Second Hopf map and supersymmetric mechanics with a Yang monopole

Gonzales, Marcelo; Kuznetsova, Z.; Nersessian, Armen; Toppan, Francesco; Yeghikyan, Vahagn

doi:10.1103/physrevd.80.025022

Cited by 22 publications

(51 citation statements)

References 40 publications

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“…Finally, the way to deal with spin degrees of freedom proposed in the present work could be relevant for a proper supersymmetric generalization of the system with Yang monopole recently analyzed in [16].…”

Section: Resultsmentioning

confidence: 99%

Potentials inN=4superconformal mechanics

Bellucci

Krivonos²

2009

Phys. Rev. D

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Proceeding from nonlinear realizations of (super)conformal symmetries, we explicitly demonstrate that adding the harmonic oscillator potential to the action of conformal mechanics does not break these symmetries but modifies the transformation properties of the (super)fields. We also analyze the possibility to introduce potentials in N = 4 supersymmetric mechanics by coupling it with auxiliary fermionic superfields. The new coupling we considered does not introduce new fermionic degrees of freedom -all our additional fermions are purely auxiliary ones. The new bosonic components have a first order kinetic term and therefore they serve as spin degrees of freedom. The resulting system contains, besides the potential term in the bosonic sector, a non-trivial spin-like interaction in the fermionic sector. The superconformal mechanics we constructed in this paper is invariant under the full D(2, 1; α) superconformal group. This invariance is not evident and is achieved within modified (super)conformal transformations of the superfields.

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Section: Resultsmentioning

confidence: 99%

Potentials inN=4superconformal mechanics

Bellucci

Krivonos²

2009

Phys. Rev. D

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“…Following [10], the word oxidation has been here consistently used in a specific and restricted sense, referring to the operation of enlarging the number of extended supersymmetries (from N to N + 1) acting on a supermultiplet with the same number of component fields. At the end it is worth mentioning a recent paper [37] in which the N = 4-invariance for a non-minimal supermultiplet in presence of a Yang monopole is discussed (see also [16]). …”

Section: Discussionmentioning

confidence: 99%

“…Non-minimal linear representations have been discussed in [4,12,13,16,17]. The maximal finite number n max of bosonic (fermionic) fields entering a non-minimal representation is given by [12,13] n max = 2 N −1 .…”

Section: Introductionmentioning

confidence: 99%

On nonminimal ${\cal N}=4$N=4 supermultiplets in 1D and their associated σ-models

Gonzales¹,

Khodaee²,

Toppan³

2011

Journal of Mathematical Physics

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We construct the non-minimal linear representations of the N = 4 Extended Supersymmetry in one-dimension. They act on 8 bosonic and 8 fermionic fields. Inequivalent representations are specified by the mass-dimension of the fields and the connectivity of the associated graphs. The oxidation to minimal N = 5 linear representations is given. Two types of N = 4 σ-models based on non-minimal representations are obtained: the resulting off-shell actions are either manifestly invariant or depend on a constrained prepotential. The connectivity properties of the graphs play a decisive role in discriminating inequivalent actions. These results find application in partial breaking of supersymmetric theories.

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“…The most natural candidate for this role is the nonlinear (4, 8, 4) supermultiplet [21,22], which would extend the number of fermions to eight. Nevertheless, we do not expect the corresponding action to enjoy N =8 supersymmetry [6], due to rather strong restrictions on the bosonic metric imposed by the four extra supersymmetries. We are planning to consider these possibilities in more detail elsewhere.…”

Section: Resultsmentioning

confidence: 99%

“…From a formal point of view, such an extension requires a supersymmetric mechanics of an isospin-carrying particle moving in the background of magnetic monopoles. By now it is well known [5,6,7,8,9,10] that to invent monopole-type interactions in Lagrangian mechanics one has to involve "isospin" variables with a specific kinetic energy of first order in the time derivatives. In supersymmetric systems these "isospin" variables become part of some supermultiplet, whose spinor components are auxiliary.…”

Section: Introductionmentioning

confidence: 99%

N=4supersymmetry and the Belavin-Polyakov-Shvarts-Tyupkin instanton

Krivonos¹,

Lechtenfeld

Sutulin³

2010

Phys. Rev. D

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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 × 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.

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Second Hopf map and supersymmetric mechanics with a Yang monopole

Cited by 22 publications

References 40 publications

Potentials inN=4superconformal mechanics

Potentials inN=4superconformal mechanics

On nonminimal ${\cal N}=4$N=4 supermultiplets in 1D and their associated σ-models

N=4supersymmetry and the Belavin-Polyakov-Shvarts-Tyupkin instanton

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