News on SU(2|1) Supersymmetric Mechanics

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 191)

Abstract

We report on a recent progress in exploring the SU(2|1) supersymmetric quantum mechanics. Our focus is on the harmonic SU(2|1) superspace formalism which provides a superfield description of the multiplet \((\mathbf{4, 4, 0})\) and its “mirror” version. We present the \(\sigma \)-model and Wess–Zumino type actions for these multiplets, in both the superfield and the component approaches. An interesting new feature as compared to the flat \(\mathcal{N}=4, d=1\) case is the absence of the explicit SU(2|1) invariant Wess–Zumino term for the ordinary \((\mathbf{4, 4, 0})\) multiplet and yet the existence of such a term for the mirror multiplet. The superconformal subclass of the SU(2|1) invariant \((\mathbf{4, 4, 0})\) actions is also described. Its main distinguishing features are the “trigonometric” realization of the \(d=1\) conformal group SO(2, 1) and the oscillator-type potential terms in the component actions.

Notes

Acknowledgements

Evgeny Ivanov thanks the organizers of the 11-th International Workshop “Lie Theory and Its Applications in Physics” and, especially, Vladimir Dobrev for the kind hospitality in Varna. The authors acknowledge a partial support from the RFBR grant 15-02-06670 and a grant of the Heisenberg - Landau program.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2016

Authors and Affiliations

  1. 1.Bogoliubov Laboratory of Theoretical PhysicsJINRDubnaRussia

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