Abstract
We present a Lagrangian formulation for \( \mathcal{N} = 4 \) supersymmetric quantummechanical systems describing the motion in external non-Abelian self-dual gauge fields. For any such system, one can write a component supersymmetric Lagrangian by introducing extra bosonic variables with topological Chern-Simons type interaction. For a special class of such system when the fields are expressed in the ‘t Hooft ansatz form, it is possible to give a superfield description using harmonic superspace formalism. As a new explicit example, the \( \mathcal{N} = 4 \) mechanics with Yang monopole is constructed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Witten, Constraints on supersymmetry breaking, Nucl. Phys. B 202 (1982) 253 [SPIRES].
A. Galperin, E. Ivanov, V. Ogievetsky and E. Sokatchev, Harmonic superspace: key to N = 2 supersymmetry theories, JETP Lett. 40 (1984) 912 [SPIRES].
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 [SPIRES].
A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic superspace, Cambridge University Press, Cambridge U.K. (2001), 306 p..
E. Ivanov and O. Lechtenfeld, N = 4 supersymmetric mechanics in harmonic superspace, JHEP 09 (2003) 073 [hep-th/0307111] [SPIRES].
L. Álvarez-Gaumé, Supersymmetry and the Atiyah-Singer index theorem, Commun. Math. Phys. 90 (1983) 161 [SPIRES].
D. Friedan and P. Windey, Supersymmetric derivation of the Atiyah-Singer index and the chiral anomaly, Nucl. Phys. B 235 (1984) 395 [SPIRES].
R. Jackiw and C. Rebbi, Conformal properties of a Yang-Mills pseudoparticle, Phys. Rev. D 14 (1976) 517 [SPIRES].
M. Konyushikhin and A.V. Smilga, Self-duality and supersymmetry, to be published in Phys. Lett. B, arXiv:0910.5162 [SPIRES].
G. ’t Hooft, Symmetry breaking through Bell-Jackiw anomalies, Phys. Rev. Lett. 37 (1976) 8 [SPIRES].
E. Corrigan and D.B. Fairlie, Scalar field theory and exact solutions to a classical SU(2) gauge theory, Phys. Lett. B 67 (1977) 69 [SPIRES].
M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld and Y.I. Manin, Construction of instantons, Phys. Lett. A 65 (1978) 185 [SPIRES].
F. Delduc and E. Ivanov, Gauging N = 4 supersymmetric mechanics, Nucl. Phys. B 753 (2006) 211 [hep-th/0605211] [SPIRES].
S. Fedoruk, E. Ivanov and O. Lechtenfeld, Supersymmetric Calogero models by gauging, Phys. Rev. D 79 (2009) 105015 [arXiv:0812.4276] [SPIRES].
S. Fedoruk, E. Ivanov and O. Lechtenfeld, OSp(4—2) superconformal mechanics, JHEP 08 (2009) 081 [arXiv:0905.4951] [SPIRES].
S. Fedoruk, E. Ivanov and O. Lechtenfeld, New D(2, 1, α) mechanics with spin variables JHEP 10 (10) 129 [arXiv:0912.3508] [SPIRES].
S. Bellucci, S. Krivonos and A. Sutulin, Three dimensional N = 4 supersymmetric mechanics with Wu-Yang monopole, arXiv:0911.3257 [SPIRES].
G.V. Dunne, Aspects of Chern-Simons theory, hep-th/9902115 [SPIRES].
A.P. Polychronakos, Integrable systems from gauged matrix models, Phys. Lett. B 266 (1991) 29 [SPIRES].
E. Ivanov, L. Mezincescu and P.K. Townsend, Fuzzy CP(n|m) as a quantum superspace, hep-th/0311159 [SPIRES].
C.N. Yang, Generalization of Dirac’s monopole to SU(2) gauge fields, J. Math. Phys. 19 (1978) 320 [SPIRES].
G.W. Gibbons and P.K. Townsend, Self-gravitating Yang monopoles in all dimensions, Class. Quant. Grav. 23 (2006) 4873 [hep-th/0604024] [SPIRES].
M. Gonzales, Z. Kuznetsova, A. Nersessian, F. Toppan and V. Yeghikyan, Second Hopf map and supersymmetric mechanics with Yang monopole, Phys. Rev. D 80 (2009) 025022 [arXiv:0902.2682] [SPIRES].
E.A. Ivanov, S.O. Krivonos and V.M. Leviant, Geometric superfield approach to superconformal mechanics, J. Phys. A 22 (1989) 4201 [SPIRES].
A. Alekseev, L.D. Faddeev and S.L. Shatashvili, Quantization of symplectic orbits of compact Lie groups by means of the functional integral, J. Geom. Phys. 5 (1988) 391 [SPIRES].
M.R. Douglas and V.A. Kazakov, Large-N phase transition in continuum QCD in two-dimensions, Phys. Lett. B 319 (1993) 219 [hep-th/9305047] [SPIRES].
P.S. Howe and P.K. Townsend, Chern-Simons quantum mechanics, Class. Quant. Grav. 7 (1990) 1655 [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 0912.3289
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Ivanov, E.A., Konyushikhin, M.A. & Smilga, A.V. SQM with non-abelian self-dual fields: harmonic superspace description. J. High Energ. Phys. 2010, 33 (2010). https://doi.org/10.1007/JHEP05(2010)033
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2010)033