Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 7 (2011), 015, 14 pages      arXiv:1102.2288      http://dx.doi.org/10.3842/SIGMA.2011.015
Contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design”

Harmonic Superfields in N=4 Supersymmetric Quantum Mechanics

Evgeny A. Ivanov
Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Moscow Region, Russia

Received December 20, 2010, in final form February 03, 2011; Published online February 11, 2011

Abstract
This is a brief survey of applications of the harmonic superspace methods to the models of N=4 supersymmetric quantum mechanics (SQM). The main focus is on a recent progress in constructing SQM models with couplings to the background non-Abelian gauge fields. Besides reviewing and systemizing the relevant results, we present some new examples and make clarifying comments.

Key words: supersymmetry; harmonic superspace; mechanics.

pdf (403 kb)   tex (20 kb)

References

  1. Witten E., Dynamical breaking of supersymmetry, Nuclear Phys. B 188 (1981), 513-554.
  2. Smilga A.V., Low-dimensional sisters of Seiberg-Witten effective theory, in From Fields to Strings: Circumnavigating Theoretical Physics, Vol. 1, Editors M. Shifman et al., World Sci. Publ., Singapore, 2005, 523-528, hep-th/0403294.
  3. Wyllard N., (Super)conformal many-body quantum mechanics with extended supersymmetry, J. Math. Phys. 41 (2000), 2826-2838, hep-th/9910160.
    Galajinsky A., Polovnikov K., Lechtenfeld O., N=4 superconformal Calogero models, J. High Energy Phys. 2007 (2007), no. 11, 008, 23 pages, arXiv:0708.1075.
    Krivonos S., Lechtenfeld O., Polovnikov K., N=4 superconformal n-particle mechanics via superspace, Nuclear Phys. B 817 (2009), 265-283, arXiv:0812.5062.
  4. Fedoruk S., Ivanov E., Lechtenfeld O., Supersymmetric Calogero models by gauging, Phys. Rev. D 79 (2009), 105015, 6 pages, arXiv:0812.4276.
  5. Ivanov E., Mezincescu L., Townsend P.K., Planar super-Landau models, J. High Energy Phys. 2006 (2006), no. 1, 143, 23 pages, hep-th/0510019.
    Curtright T., Mezincescu L., Ivanov E., Townsend P.K., Planar super-Landau models revisited, J. High Energy Phys. 2007 (2007), no. 4, 020, 25 pages, hep-th/0612300.
  6. Gates S.J., Jr., Rana L., Ultra-multiplets: a new representation of rigid 2D, N=8 supersymmetry, Phys. Lett. B 342 (1995), 132-137, hep-th/9410150.
    Pashnev A., Toppan F., On the classification of N-extended supersymmetric quantum mechanical systems, J. Math. Phys. 42 (2001), 5257-5271, hep-th/0010135.
  7. Ivanov E., Krivonos S., Lechtenfeld O., N=4, d=1 supermultiplets from nonlinear realizations of D(2,1;a), Classical Quantum Gravity 21 (2004), 1031-1050, hep-th/0310299.
  8. Ivanov E., Lechtenfeld O., N=4 supersymmetric mechanics in harmonic superspace, J. High Energy Phys. 2003 (2003), no. 9, 073, 33 pages, hep-th/0307111.
  9. Galperin A., Ivanov E., Ogievetsky V., Sokatchev E., Harmonic superspace: key to N=2 supersymmetric theories, JETP Lett. 40 (1984), 912-916.
    Galperin A., Ivanov E., Kalitzin S., Ogievetsky V., Sokatchev E., Unconstrained N=2 matter, Yang-Mills and supergravity theories in harmonic superspace, Classical Quantum Gravity 1 (1984), 469-498.
  10. Galperin A.S., Ivanov E.A., Ogievetsky V.I., Sokatchev E.S., Harmonic superspace, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 2001.
  11. Ivanov E.A., Supersymmetry in superspace: 35 years of the research activity in LTP, Phys. Part. Nuclei 40 (2009), 291-306, hep-th/0609176.
  12. Delduc F., Ivanov E., Gauging N=4 supersymmetric mechanics, Nuclear Phys. B 753 (2006), 211-241, hep-th/0605211.
  13. Delduc F., Ivanov E., Gauging N=4 supersymmetric mechanics. II. (1,4,3) models from the (4,4,0) ones, Nuclear Phys. B 770 (2007), 179-205, hep-th/0611247.
  14. Delduc F., Ivanov E., The common origin of linear and nonlinear chiral multiplets in N=4 mechanics, Nuclear Phys. B 787 (2007), 176-197, arXiv:0706.0706.
  15. Sonner J., Tong D., Berry phase and supersymmetry, J. High Energy Phys. 2009 (2009), no. 1, 063, 9 pages, arXiv:0810.1280.
  16. Gonzales M., Kuznetsova Z., Nersessian A., Toppan F., Yeghikyan V., Second Hopf map and supersymmetric mechanics with a Yang monopole, Phys. Rev. D 80 (2009), 025022, 13 pages, arXiv:0902.2682.
  17. Dunne G.V., Jackiw R., Trugenberger C.A., "Topological" (Chern-Simons) quantum mechanics, Phys. Rev. D 14 (1990), 661-666.
    Howe P.S., Townsend P.K., Chern-Simons quantum mechanics, Classical Quantum Gravity 7 (1990), 1655-1668.
  18. Feher L., Horváthy P.A., O'Raifeartaigh L., Applications of chitral supersymetry to spin fields in selfdual backgrounds, Internat. J. Modern Phys. A 4 (1989), 5277-5285, arXiv:0903.2920.
  19. Konyushikhin M., Smilga A.V., Self-duality and supersymmetry, Phys. Lett. B 689 (2010), 95-100, arXiv:0910.5162.
  20. Ivanov E.A., Konyushikhin M.A., Smilga A.V., SQM with non-Abelian self-dual fields: harmonic superspace description, J. High Energy Phys. 2010 (2010), no. 5, 033, 14 pages, arXiv:0912.3289.
  21. Ivanov E., Konyushikhin M., N=4, 3D supersymmetric quantum mechnics in non-Abelian monopole background, Phys. Rev. D 82 (2010), 085014, 8 pages, arXiv:1004.4597.
  22. Bellucci S., Krivonos S., Sutulin A., Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole, Phys. Rev. D 81 (2010), 105026, 9 pages, arXiv:0911.3257.
  23. Krivonos S., Lechtenfeld O., Sutulin A., N=4 supersymmetry and the Belavin-Polyakov-Shvarts-Tyupkin instanton, Phys. Rev. D 81 (2010), 085021, 7 pages, arXiv:1001.2659.
  24. Kirchberg A., Länge J.D., Wipf A., Extended supersymmetries and the Dirac operator, Ann. Physics 315 (2005), 467-487, hep-th/0401134.
  25. Ivanov E., Niederle J., Bi-harmonic superspace for N=4 mechanics, Phys. Rev. D 80 (2009), 065027, 23 pages, arXiv:0905.3770.
  26. Rocek M., Verlinde E.P., Duality, quotients, and currents, Nuclear Phys. B 373 (1992), 630-646, hep-th/9110053.
  27. Galperin A., Ivanov E., Ogievetsky V., Sokatchev E., Gauge field geometry from complex and harmonic analyticities. I. Kähler and self-dual Yang-Mills cases, Ann. Physics 185 (1988), 1-21.
  28. Yang C.N., Generalization of Dirac's monopole to SU2 gauge fields, J. Math. Phys. 19 (1978), 320-328.
  29. Polychronakos A.P., Integrable systems from gauged matrix models, Phys. Lett. B 266 (1991), 29-34.
  30. de Crombrugghe M., Rittenberg V., Supersymmetric quantum mechanics, Ann. Physics 151 (1983), 99-126.
  31. Wu T.T., Yang C.N., Some solutions of the classical isotopic gauge field equations, in Properties of Matter Under Unusual Conditions, Editors H. Mark and S. Fernbach, Interscience, New York, 1969, 345-349.

Previous article   Next article   Contents of Volume 7 (2011)