N=4, d=1 supersymmetric hyper-Kähler sigma models with isospin variables

Bellucci, Stefano; Krivonos, S.; Sutulin, A.

doi:10.1007/jhep02(2011)038

Cited by 3 publications

(3 citation statements)

References 44 publications

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“…Finally we note that it is possible and interesting to extend our results to higher dimensional N = 4 mechanics describing, for example, the particle moving over the CP n manifold in the background of the magnetic field of some monopole [9]. Indeed, our analysis shows that the N = 4 supersymmetrizations we performed preserve the initial SU (1, 1) and/or SU (2) symmetry of the bosonic core.…”

Section: Resultsmentioning

confidence: 62%

“…The most essential feature of such a coupling is that it has to be a first-order kinetic term for the isospin variables. The approach, which we will follow in this Letter, has been elaborated in [6,7,8,9]. There, isospin variables and auxiliary fermions were put in a doublet of fermionic superfields {Ξ i , Ξ i } subjected to the irreducible conditions [10]…”

Section: Superspace Actionmentioning

confidence: 99%

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N=4chiral supermultiplet interacting with a magnetic field

et al. 2012

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We couple N = 4 chiral supermultiplet with an auxiliary N = 4 fermionic supermutiplet containing on-shell four physical fermions and four auxiliary bosons. The latter ones play the role of isospin variables. We choose the very specific coupling which results in a component action containing only time derivatives of fermionic components presented in the auxiliary supermultiplet, which therefore may be dualized into auxiliary ones. The resulting component action describes the interaction of the chiral supermultiplet with a magnetic field constant on the pseudo-sphere SU (1, 1)/U (1). Then we specify the prepotential of our theory to get, in the bosonic sector, the action for the particle moving over the pseudo-sphere -Lobachevsky space. We provided also the Hamiltonian formulation of this system and show that the full symmetry group of our system is SU (1, 1) × U (1). The currents forming the su(1, 1) algebra are modified, as compared to the bosonic case, by the fermionic and isospin terms, while the additional u(1) current contains only isospin variables.One of the most important features of our construction is the presence in the Hamiltonian and supercharges of all currents of the isospin group SU (2). Despite the fact that two of the su(2) currents {T, T } enter the Hamiltonian only through the Casimir operator of the SU (2) group, they cannot be dropped out, even after fixing the total isospin of the system, because these currents themselves enter into the supercharges.We also present the Hamiltonian and supercharges describing the motion of a particle over the sphere S 2 in the background of constant magnetic field. In this case the additional isospin currents form the su(1, 1) algebra.

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Section: Resultsmentioning

confidence: 62%

Section: Superspace Actionmentioning

confidence: 99%

N=4chiral supermultiplet interacting with a magnetic field

et al. 2012

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“…Supersymmetric extensions factorize as well and each factor can be extended to D(2, 1; λ) [41]. Another motivation is to investigate the connection between the spectra of N = 4 superconformal quantum mechanical models that have been studied in recent years [42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64] and the deformations of minimal unitary supermultiplets of corresponding conformal superalgebras in the light of the results of [40,19].…”

Section: Introductionmentioning

confidence: 99%

Minimal unitary representation of D(2,1;λ) and its SU(2) deformations and d=1, N=4 superconformal models

Govil,

Gunaydin

2012

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Quantization of the geometric quasiconformal realizations of noncompact groups and supergroups leads directly to their minimal unitary representations (minreps). Using quasiconformal methods massless unitary supermultiplets of superconformal groups SU (2, 2|N ) and OSp(8 * |2n) in four and six dimensions were constructed as minreps and their U (1) and SU (2) deformations, respectively. In this paper we extend these results to SU (2) deformations of the minrep of N = 4 superconformal algebra D(2, 1; λ) in one dimension. We find that SU (2) deformations can be achieved using n pairs of bosons and m pairs of fermions simultaneously. The generators of deformed minimal representations of D(2, 1; λ) commute with the generators of a dual superalgebra OSp(2n * |2m) realized in terms of these bosons and fermions. We show that there exists a precise mapping between symmetry generators of N = 4 superconformal models in harmonic superspace studied recently and minimal unitary supermultiplets of D(2, 1; λ) deformed by a pair of bosons. This can be understood as a particular case of a general mapping between the spectra of quantum mechanical quaternionic Kähler sigma models with eight super symmetries and minreps of their isometry groups that descends from the precise mapping established between the 4d, N = 2 sigma models coupled to supergravity and minreps of their isometry groups.

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Minimal unitary representation of and its deformations and , superconformal models

Govil

Günaydın

2013

Nuclear Physics B

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N=4, d=1 supersymmetric hyper-Kähler sigma models with isospin variables

Cited by 3 publications

References 44 publications

N=4chiral supermultiplet interacting with a magnetic field

N=4chiral supermultiplet interacting with a magnetic field

Minimal unitary representation of D(2,1;λ) and its SU(2) deformations and d=1, N=4 superconformal models

Minimal unitary representation of and its deformations and , superconformal models

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