The European Physical Journal C

, 72:2144 | Cite as

New superalgebras in supersymmetric U(1) gauge theory

  • Reza AbbaspurEmail author
Regular Article - Theoretical Physics


Noncommutative generalizations of a supersymmetry algebra in two dimensions have been introduced earlier in Abbaspur (Int. J. Mod. Phys. A 18:855–878, 2003; Mod. Phys. Lett. A 18:587–599, 2003). In this paper we present a field theoretic realization for these algebras in the context of \(\mathcal{N}=1\) supersymmetric U(1) gauge theories in two dimensions. We also describe a possible generalization to 4-dimensional theories.


Gauge Theory Gauge Transformation Finite Order Gauge Parameter Supersymmetry Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I would like to deeply thank my father, Mohammad Hossein Abbaspour-Tamijani, for his genuine concern and encouragements. I would also like to thank the referees of European Physical Journal C for their valuable comments that have led to improvement of this paper.


  1. 1.
    N. Seiberg, E. Witten, String theory and noncommutative geometry. J. High Energy Phys. 9909, 032 (1999). arXiv:hep-th/9908142 MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    M.R. Douglas, N.A. Nekrasov, Noncommutative field theory. Rev. Mod. Phys. 73, 977–1029 (2002). arXiv:hep-th/0106048 MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    R.J. Szabo, Quantum field theory on noncommutative spaces. Phys. Rep. 378, 207–299 (2003). arXiv:hep-th/0109162 MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    N. Seiberg, A note on background independence in noncommutative gauge theories, matrix model and tachyon condensation. J. High Energy Phys. 0009, 003 (2000). arXiv:hep-th/0008013 MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    C.-S. Chu, F. Zamora, Manifest supersymmetry in non-commutative geometry. J. High Energy Phys. 0002, 022 (2000). arXiv:hep-th/9912153 MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    J. Bagger, I. Giannakis, Spacetime supersymmetry in a nontrivial NS-NS superstring background. Phys. Rev. D 65, 046002 (2002). arXiv:hep-th/0107260 MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    J. de Boer, P.A. Grassi, P. van Nieuwenhuizen, Non-commutative superspace from string theory. Phys. Lett. B 574, 98–104 (2003). arXiv:hep-th/0302078 MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    H. Ooguri, C. Vafa, The C-deformation of gluino and non-planar diagrams. Adv. Theor. Math. Phys. 7, 53 (2003). arXiv:hep-th/0302109 MathSciNetGoogle Scholar
  9. 9.
    H. Ooguri, C. Vafa, Gravity induced C-deformation. Adv. Theor. Math. Phys. 7, 405 (2004). arXiv:hep-th/0303063 MathSciNetGoogle Scholar
  10. 10.
    N. Seiberg, Noncommutative superspace, N=1/2 supersymmetry, field theory and string theory. J. High Energy Phys. 0306, 010 (2003). arXiv:hep-th/0305248 ADSCrossRefGoogle Scholar
  11. 11.
    N. Berkovits, N. Seiberg, Superstrings in graviphoton background and N=1/2+3/2 supersymmetry. J. High Energy Phys. 0307, 010 (2003). arXiv:hep-th/0306226 MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    K. Ito, S. Sasaki, Non(anti)commutative N=2 supersymmetric gauge theory from superstrings in the graviphoton background. J. High Energy Phys. 0611, 004 (2006). arXiv:hep-th/0608143 MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    P. Kosinski, J. Lukierski, P. Maslanka, Quantum deformations of space-time SUSY and noncommutative superfield theory. arXiv:hep-th/0011053
  14. 14.
    T. Pengpan, X. Xiong, A note on the non-commutative Wess–Zumino model. Phys. Rev. D 63, 085012 (2001). arXiv:hep-th/0009070 MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    S. Terashima, A note on superfields and noncommutative geometry. Phys. Lett. B 482, 276–282 (2000). arXiv:hep-th/0002119 MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    S. Ferrara, M.A. Lledó, Some aspects of deformations of supersymmetric field theories. J. High Energy Phys. 0005, 008 (2000). arXiv:hep-th/0002084 ADSCrossRefGoogle Scholar
  17. 17.
    M.A. Lledó, Supersymmetric field theories on deformed space-time. arXiv:hep-th/0011268
  18. 18.
    S. Ferrara, M.A. Lledo, O. Macia, Supersymmetry in noncommutative superspaces. arXiv:hep-th/0307039
  19. 19.
    D. Klemm, S. Penati, L. Tamassia, Non(anti)commutative superspace. arXiv:hep-th/0104190
  20. 20.
    S. Paban, S. Sethi, M. Stern, Non-commutativity and supersymmetry. J. High Energy Phys. 0203, 012 (2002). arXiv:hep-th/0201259 MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    R. Abbaspur, Noncommutative supersymmetry in two dimensions. Int. J. Mod. Phys. A 18, 855–878 (2003). arXiv:hep-th/0110005 MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. 22.
    R. Abbaspur, Generalized noncommutative superalgebras. Mod. Phys. Lett. A 18, 587–599 (2003) MathSciNetADSzbMATHCrossRefGoogle Scholar
  23. 23.
    R. Abbaspur, Realization of central charges in theories with generalized noncommutative supersymmetry. J. High Energy Phys. 05, 023 (2003) MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    S. James Gates Jr. et al., Superspace: one Thousand and One Lessons in Supersymmetry (Benjamin/Cummings, London, 1983) zbMATHGoogle Scholar
  25. 25.
    J. Wess, J. Bagger, Supersymmetry and Supergravity, 2nd edn. (Princeton University Press, Princeton, 1992) Google Scholar
  26. 26.
    A. Bilal, Introduction to supersymmetry. arXiv:hep-th/0101055
  27. 27.
    E. Witten, D. Olive, Supersymmetry algebras that include topological charges. Phys. Lett. B 78, 97 (1978) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2012

Authors and Affiliations

  1. 1.Department of Physics, School of SciencesTarbiat Modares UniversityTehranIran

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