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Journal of High Energy Physics

, 2016:103 | Cite as

Gauged spinning models with deformed supersymmetry

  • Sergey Fedoruk
  • Evgeny Ivanov
Open Access
Regular Article - Theoretical Physics

Abstract

New models of the SU(2|1) supersymmetric mechanics based on gauging the systems with dynamical (1, 4, 3) and semi-dynamical (4, 4, 0) supermultiplets are presented. We propose a new version of SU(2|1) harmonic superspace approach which makes it possible to construct the Wess-Zumino term for interacting (4,4,0) multiplets. A new \( \mathcal{N}=4 \) extension of d = 1 Calogero-Moser multiparticle system is obtained by gauging the U(n) isometry of matrix SU(2|1) harmonic superfield model.

Keywords

Extended Supersymmetry Superspaces Supersymmetric gauge theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    E. Ivanov and S. Sidorov, Deformed Supersymmetric Mechanics, Class. Quant. Grav. 31 (2014) 075013 [arXiv:1307.7690] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    E. Ivanov and S. Sidorov, Super Kähler oscillator from SU(2|1) superspace, J. Phys. A 47 (2014) 292002 [arXiv:1312.6821] [INSPIRE].MathSciNetMATHGoogle Scholar
  3. [3]
    E. Ivanov and S. Sidorov, SU(2|1) mechanics and harmonic superspace, Class. Quant. Grav. 33 (2016) 055001 [arXiv:1507.00987] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    A.V. Smilga, Weak supersymmetry, Phys. Lett. B 585 (2004) 173 [hep-th/0311023] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    S. Bellucci and A. Nersessian, (Super)oscillator on CP N and constant magnetic field, Phys. Rev. D 67 (2003) 065013 [Erratum ibid. D 71 (2005) 089901] [hep-th/0211070] [INSPIRE].
  6. [6]
    S. Bellucci and A. Nersessian, Supersymmetric Kähler oscillator in a constant magnetic field, hep-th/0401232 [INSPIRE].
  7. [7]
    G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    T.T. Dumitrescu, G. Festuccia and N. Seiberg, Exploring Curved Superspace, JHEP 08 (2012) 141 [arXiv:1205.1115] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    I.B. Samsonov and D. Sorokin, Superfield theories on S 3 and their localization, JHEP 04 (2014) 102 [arXiv:1401.7952] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    I.B. Samsonov and D. Sorokin, Gauge and matter superfield theories on S 2, JHEP 09 (2014) 097 [arXiv:1407.6270] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    E. Ivanov and O. Lechtenfeld, N = 4 supersymmetric mechanics in harmonic superspace, JHEP 09 (2003) 073 [hep-th/0307111] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    E. Ivanov, O. Lechtenfeld and S. Sidorov, SU(2|2) supersymmetric mechanics, JHEP 11 (2016) 031 [arXiv:1609.00490] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    S. Fedoruk, E. Ivanov and O. Lechtenfeld, Supersymmetric Calogero models by gauging, Phys. Rev. D 79 (2009) 105015 [arXiv:0812.4276] [INSPIRE].ADSMathSciNetGoogle Scholar
  14. [14]
    S. Fedoruk, E. Ivanov and O. Lechtenfeld, OSp(4|2) Superconformal Mechanics, JHEP 08 (2009) 081 [arXiv:0905.4951] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    S. Fedoruk, E. Ivanov and O. Lechtenfeld, New D(2, 1; α) Mechanics with Spin Variables, JHEP 04 (2010) 129 [arXiv:0912.3508] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    S. Fedoruk, E. Ivanov and O. Lechtenfeld, Superconformal Mechanics, J. Phys. A 45 (2012) 173001 [arXiv:1112.1947] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  17. [17]
    F. Delduc and E. Ivanov, Gauging N = 4 Supersymmetric Mechanics, Nucl. Phys. B 753 (2006) 211 [hep-th/0605211] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    F. Delduc and E. Ivanov, Gauging N = 4 supersymmetric mechanics II: (1, 4, 3) models from the (4, 4, 0) ones, Nucl. Phys. B 770 (2007) 179 [hep-th/0611247] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    F. Calogero, Solution of a three-body problem in one-dimension, J. Math. Phys. 10 (1969) 2191 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    F. Calogero, Ground state of one-dimensional N body system, J. Math. Phys. 10 (1969) 2197 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    F. Calogero, Solution of the one-dimensional N body problems with quadratic and/or inversely quadratic pair potentials, J. Math. Phys. 12 (1971) 419 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    J. Moser, Three integrable Hamiltonian systems connnected with isospectral deformations, Adv. Math. 16 (1975) 197 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  23. [23]
    A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace, Class. Quant. Grav. 1 (1984) 469 [Erratum ibid. 2 (1985) 127] [INSPIRE].
  24. [24]
    A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic Superspace, Cambridge University Press (2001).Google Scholar
  25. [25]
    A. Galperin, E. Ivanov and O. Ogievetsky, Harmonic space and quaternionic manifolds, Annals Phys. 230 (1994) 201 [hep-th/9212155] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    J. Gibbons and T. Hermsen, A generalization of the Calogero-Moser system, Physica D 11 (1984) 337.ADSMathSciNetMATHGoogle Scholar
  27. [27]
    S. Wojciechowski, An integrable marriade of the Euler equations with the Calogero-Moser system, Phys. Lett. A 111 (1985) 101.ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    A.P. Polychronakos, Generalized Calogero models through reductions by discrete symmetries, Nucl. Phys. B 543 (1999) 485 [hep-th/9810211] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    A.P. Polychronakos, Calogero-Moser models with noncommutative spin interactions, Phys. Rev. Lett. 89 (2002) 126403 [hep-th/0112141] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    A.P. Polychronakos, Physics and Mathematics of Calogero particles, J. Phys. A 39 (2006) 12793 [hep-th/0607033] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  31. [31]
    G.W. Gibbons and P.K. Townsend, Black holes and Calogero models, Phys. Lett. B 454 (1999) 187 [hep-th/9812034] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    G. Papadopoulos, New potentials for conformal mechanics, Class. Quant. Grav. 30 (2013) 075018 [arXiv:1210.1719] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  33. [33]
    N.L. Holanda and F. Toppan, Four types of (super)conformal mechanics: D-module reps and invariant actions, J. Math. Phys. 55 (2014) 061703 [arXiv:1402.7298] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    E. Ivanov, S. Sidorov and F. Toppan, Superconformal mechanics in SU(2|1) superspace, Phys. Rev. D 91 (2015) 085032 [arXiv:1501.05622] [INSPIRE].ADSMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Bogoliubov Laboratory of Theoretical Physics, JINRDubnaRussia

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