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Aspects of ABJ theory

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Abstract

In this paper we will analyse the deformation of a ABJ theory in harmonic superspace. So, we will first discuss deformations of the harmonic superspace caused by a graviphoton background. We will then study the ABJ theory in this noncommutative superspace. This deformed ABJ theory will be shown to posses \( \mathcal{N} \) = 6 supersymmetry. We also discuss the BRST symmetry of this theory.

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References

  1. A.S. Galperin et al., Harmonic superspace, Cambridge University Press, Camrbridge U.K. (2001).

    Book  MATH  Google Scholar 

  2. A. Galperin et al., Unconstrained N = 2 matter, Yang-Mills and supergravity theories in harmonic superspace, Class. Quant. Grav. 1 (1984) 469.

    Article  MathSciNet  ADS  Google Scholar 

  3. A. Galperin et al., Harmonic superspace: key to N = 2 supersymmetry theories, JETP Lett. 40 (1984) 912 [Pisma Zh. Eksp. Teor. Fiz. 40 (1984) 155] [INSPIRE].

  4. B.M. Zupnik, Harmonic superspaces for three-dimensional theories, in Supersymmetries and quantum symmetries, J. Wess and E. Ivanov eds., Springer Lecture Notes in Physics volume 524, Springer U.S.A. (1998).

  5. B. Zupnik and D. Khetselius, Three-dimensional extended supersymmetry in the harmonic superspace (in Russian), Sov. J. Nucl. Phys. 47 (1988) 730 [INSPIRE].

    Google Scholar 

  6. I. Buchbinder et al., ABJM models in N = 3 harmonic superspace, JHEP 03 (2009) 096 [arXiv:0811.4774] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M 2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. M. Naghdi, A monopole instanton-like effect in the ABJM model, Int. J. Mod. Phys. A 26 (2011) 3259 [arXiv:1106.0907] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  9. A. Gustavsson, Monopoles, three-algebras and ABJM theories with N = 5, 6, 8 supersymmetry, JHEP 01 (2011) 037 [arXiv:1012.4568] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. M. Faizal, M -theory in the gaugeon formalism, Commun. Theor. Phys. 57 (2012) 637 [arXiv:1201.1220] [INSPIRE].

    Article  MATH  Google Scholar 

  11. M. Faizal, M-theory on deformed superspace, Phys. Rev. D 84 (2011) 106011 [arXiv:1111.0213] [INSPIRE].

    ADS  Google Scholar 

  12. J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  13. J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  14. J. Bagger and N. Lambert, Comments on multiple M2-branes, JHEP 02 (2008) 105 [arXiv:0712.3738] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. O.-K. Kwon, P. Oh and J. Sohn, Notes on supersymmetry enhancement of ABJM theory, JHEP 08 (2009) 093 [arXiv:0906.4333] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. H. Samtleben and R. Wimmer, N = 6 superspace constraints, SUSY enhancement and monopole operators, JHEP 10 (2010) 080 [arXiv:1008.2739] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. S. Cremonesi, Type IIB construction of flavoured ABJ(M) and fractional M2 branes, JHEP 01 (2011) 076 [arXiv:1007.4562] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. J. Evslin and S. Kuperstein, ABJ(M) and fractional M2’s with fractional M2 charge, JHEP 12 (2009) 016 [arXiv:0906.2703] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. J. Minahan, O. Ohlsson Sax and C. Sieg, Magnon dispersion to four loops in the ABJM and ABJ models, J. Phys. A 43 (2010) 275402 [arXiv:0908.2463] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  22. P. Caputa, C. Kristjansen and K. Zoubos, Non-planar ABJ theory and parity, Phys. Lett. B 677 (2009) 197 [arXiv:0903.3354] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  23. B. Safarzadeh, On the Seiberg-Witten map of N = 2 SYM theory in non(anti)commutative harmonic superspace, Phys. Lett. B 601 (2004) 81 [hep-th/0406204] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  24. A. Ferrari, M. Gomes, J. Nascimento, A.Y. Petrov and A. da Silva, The three-dimensional non-anticommutative superspace, Phys. Rev. D 74 (2006) 125016 [hep-th/0607087] [INSPIRE].

    ADS  Google Scholar 

  25. N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. M.R. Douglas and N.A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2001) 977 [hep-th/0106048] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. S. Doplicher, K. Fredenhagen and J.E. Roberts, The quantum structure of space-time at the Planck scale and quantum fields, Commun. Math. Phys. 172 (1995) 187 [hep-th/0303037] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. A. Connes, Non commutative geometry, Academic Press Inc., London U.K. (1990).

    Google Scholar 

  29. J. de Boer, P.A. Grassi and P. van Nieuwenhuizen, Noncommutative superspace from string theory, Phys. Lett. B 574 (2003) 98 [hep-th/0302078] [INSPIRE].

    ADS  Google Scholar 

  30. K. Ito and S. Sasaki, Non(anti)commutative N = 2 supersymmetric gauge theory from superstrings in the graviphoton background, JHEP 11 (2006) 004 [hep-th/0608143] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. K. Ito, Y. Kobayashi and S. Sasaki, Deformation of N = 4 super Yang-Mills theory in graviphoton background, JHEP 04 (2007) 011 [hep-th/0612267] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. P. Meessen and T. Ortín, Godel space-times, Abelian instantons, the graviphoton background and other flacuum solutions, Nucl. Phys. B 684 (2004) 235 [hep-th/0401005] [INSPIRE].

    Article  ADS  Google Scholar 

  33. N. Berkovits and N. Seiberg, Superstrings in graviphoton background and N = 1/2 + 3/2 supersymmetry, JHEP 07 (2003) 010 [hep-th/0306226] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. H. Ooguri and C. Vafa, The C deformation of gluino and nonplanar diagrams, Adv. Theor. Math. Phys. 7 (2003) 53 [hep-th/0302109] [INSPIRE].

    MathSciNet  Google Scholar 

  35. N. Seiberg, Noncommutative superspace, N = 1/2 supersymmetry, field theory and string theory, JHEP 06 (2003) 010 [hep-th/0305248] [INSPIRE].

    Article  ADS  Google Scholar 

  36. E. Chang-Young, H. Kim and H. Nakajima, Noncommutative superspace and super Heisenberg group, JHEP 04 (2008) 004 [arXiv:0711.4663] [INSPIRE].

    Article  ADS  Google Scholar 

  37. K. Araki, T. Inami, H. Nakajima and Y. Saito, Quantum corrections in 2D SUSY CP N−1 σ-model on noncommutative superspace, JHEP 01 (2006) 109 [hep-th/0508061] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. J.S. Cook, Gauged Wess-Zumino model in noncommutative Minkowski superspace, J. Math. Phys. 47 (2006) 012304 [hep-th/0505247] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. Y. Kobayashi and S. Sasaki, Non-local Wess-Zumino model on nilpotent noncommutative superspace, Phys. Rev. D 72 (2005) 065015 [hep-th/0505011] [INSPIRE].

    ADS  Google Scholar 

  40. M. Faizal, Deformation of the ABJM theory, Europhys. Lett. 98 (2012) 31003.

    Article  ADS  Google Scholar 

  41. R. Auzzi and S.P. Kumar, Non-abelian vortices at weak and strong coupling in mass deformed ABJM theory, JHEP 10 (2009) 071 [arXiv:0906.2366] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. S. Mukhi and C. Papageorgakis, M 2 to D2, JHEP 05 (2008) 085.

    Article  MathSciNet  ADS  Google Scholar 

  43. Y. Pang and T. Wang, From N M 2’s to N D2’s, Phys. Rev. D 78 (2008) 125007 [arXiv:0807.1444] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  44. T. Li, Y. Liu and D. Xie, Multiple D2-brane action from M2-branes, Int. J. Mod. Phys. A 24 (2009) 3039 [arXiv:0807.1183] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  45. J.P. Allen and D.J. Smith, Coupling M2-branes to background fields, JHEP 08 (2011) 078 [arXiv:1104.5397] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. S.V. Ketov and S. Kobayashi, Higher-derivative gauge interactions of Bagger-Lambert-Gustavsson theory in \( \mathcal{N} \) = 1 superspace, Phys. Rev. D 83 (2011) 045003 [arXiv:1010.0752] [INSPIRE].

    ADS  Google Scholar 

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  1. Mathematical Institute, University of Oxford, Oxford, OX1 3LB, U.K.

    Mir Faizal

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Faizal, M. Aspects of ABJ theory. J. High Energ. Phys. 2013, 156 (2013). https://doi.org/10.1007/JHEP01(2013)156

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