Are<i>N</i>= 1 and<i>N</i>= 2 supersymmetric quantum mechanics equivalent?

Combescure, Monique; Gieres, François; Kibler, M.

doi:10.1088/0305-4470/37/43/025

Cited by 34 publications

(43 citation statements)

References 17 publications

(23 reference statements)

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“…Since the aforementioned zero modes play a crucial role towards the formulation of the quantum theory of supersymmetric Chern-Simons vortices, in this paper we shall present an interesting property of the zero modes of models with global N = 2 spacetime supersymmetry. Particularly, we find that the zero modes of fermionic and bosonic fluctuations of Abelian gauge models having a global N = 2 spacetime supersymmetry in (2 + 1)-dimensions, can separately constitute two N = 2, d = 1 supersymmetric quantum algebras [15][16][17][18][19][20][21][22], with the zero modes being the corresponding quantum Hilbert space vectors. Moreover, due to the N = 2 global spacetime supersymmetry of the theory, the underlying one dimensional N = 2 supersymmetric quantum algebras can form a centrally extended N = 4, d = 1 supersymmetric quantum algebra.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Chern–Simons vortex systems and extended supersymmetric quantum mechanics algebras

Oikonomou

2013

Nuclear Physics B

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We study N = 2 supersymmetric Chern-Simons Higgs models in (2+1)-dimensions and the existence of extended underlying supersymmetric quantum mechanics algebras. Our findings indicate that the fermionic zero modes quantum system in conjunction with the system of zero modes corresponding to bosonic fluctuations, are related to an N = 4 extended 1-dimensional supersymmetric algebra with central charge, a result closely connected to the N = 2 spacetime supersymmetry of the total system. We also add soft supersymmetric terms to the fermionic sector in order to examine how this affects the index of the corresponding Dirac operator, with the latter characterizing the degeneracy of the solitonic solutions. In addition, we analyze the impact of the underlying supersymmetric quantum algebras to the zero mode bosonic fluctuations. This is relevant to the quantum theory of self-dual vortices and particularly for the symmetries of the metric of the space of vortices solutions and also for the non-zero mode states of bosonic fluctuations.

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Section: Introductionmentioning

confidence: 99%

Supersymmetric Chern–Simons vortex systems and extended supersymmetric quantum mechanics algebras

Oikonomou

2013

Nuclear Physics B

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“…It is also shown in Reference [50] that it is equivalent to another supersymmetric system with two real supercharges: this is the reason for the N = 2 in the title.…”

Section: Introductionmentioning

confidence: 95%

“…In the classification of Supersymmetric Quantum Mechanics given by Kibler et al in [50] our formalism ranks in the class of a complex super-charge,Q, with an involution operatorF 2 = I. It is also shown in Reference [50] that it is equivalent to another supersymmetric system with two real supercharges: this is the reason for the N = 2 in the title.…”

Section: Introductionmentioning

confidence: 98%

On the Supersymmetric Spectra of two Planar Integrable Quantum Systems

Leon¹

2012

Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics

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Two planar supersymmetric quantum mechanical systems built around the quantum integrable Kepler/Coulomb and Euler/Coulomb problems are analyzed in depth. The supersymmetric spectra of both systems are unveiled, profiting from symmetry operators not related to invariance with respect to rotations. It is shown analytically how the first problem arises at the limit of zero distance between the centers of the second problem. It appears that the supersymmetric modified Euler/Coulomb problem is a quasi-isospectral deformation of the supersymmetric Kepler/Coulomb problem.

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“…The structure behind the N = 1 supersymmetry in quantum mechanics is generated by a Hermitian supercharge Q and Hermitian operator K squaring to 1 which distinguishes the "bosonic" and "fermionic" sectors [23]. In particular, these operators implement the algebra…”

Section: Supersymmetrymentioning

confidence: 99%

Supersymmetry in the Majorana Cooper-pair box

et al. 2014

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Over the years, supersymmetric quantum mechanics has evolved from a toy model of high-energy physics to a field of its own. Although various examples of supersymmetric quantum mechanics have been found, systems that have a natural realization are scarce. Here, we show that the extension of the conventional Cooper-pair box by a 4π -periodic Majorana-Josephson coupling realizes supersymmetry for a certain characteristic ratio of the conventional Josephson to the Majorana-Josephson coupling strength. The supersymmetry we find is a "hidden" minimally bosonized supersymmetry that provides a nontrivial generalization of the supersymmetry of the free particle and relies crucially on the presence of an anomalous Josephson junction in the system. We show that the resulting degeneracy of the energy levels can be probed directly in a tunneling experiment and discuss the various transport signatures. An observation of the predicted level degeneracy would provide clear evidence for the presence of a Majorana-Josephson coupling of the characteristic strength.

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AreN= 1 andN= 2 supersymmetric quantum mechanics equivalent?

Abstract: After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.

Cited by 34 publications

References 17 publications

Supersymmetric Chern–Simons vortex systems and extended supersymmetric quantum mechanics algebras

Supersymmetric Chern–Simons vortex systems and extended supersymmetric quantum mechanics algebras

On the Supersymmetric Spectra of two Planar Integrable Quantum Systems

Supersymmetry in the Majorana Cooper-pair box

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