Infrared stability of ABJ-like theories

  • Marco S. Bianchi
  • Silvia Penati
  • Massimo Siani


We consider marginal deformations of the superconformal ABJM/ABJ models which preserve \( \mathcal{N} = 2 \) supersymmetry. We determine perturbatively the spectrum of fixed points and study their infrared stability. We find a closed line of fixed points which is IR stable. The fixed point corresponding to the ABJM/ABJ models is stable under marginal deformations which respect the original SU(2) A × SU(2) B invariance, while deformations which break this group destabilize the theory which then flows to a less symmetric fixed point. We discuss the addition of flavor degrees of freedom. We prove that in general a flavor marginal superpotential does not destabilize the system in the IR. An exception is represented by a marginal coupling which mixes matter charged under different gauge sectors. Finally, we consider the case of relevant deformations which should drive the system to a strongly coupled IR fixed point recently investigated in arXiv:0909.2036 [hep-th].


Supersymmetric gauge theory Chern-Simons Theories 


  1. [1]
    J.H. Schwarz, Superconformal Chern-Simons theories, JHEP 11 (2004) 078 [hep-th/0411077] [SPIRES].CrossRefADSGoogle Scholar
  2. [2]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  3. [3]
    A. Gustavsson and S.-J. Rey, Enhanced N = 8 supersymmetry of ABJM theory on R(8) and R(8)/Z(2), arXiv:0906.3568 [SPIRES].
  4. [4]
    J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [SPIRES].MathSciNetADSGoogle Scholar
  5. [5]
    A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  6. [6]
    J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [SPIRES].MathSciNetADSGoogle Scholar
  7. [7]
    O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  8. [8]
    N. Akerblom, C. Sämann and M. Wolf, Marginal deformations and 3-algebra structures, Nucl. Phys. B 826 (2010) 456 [arXiv:0906.1705] [SPIRES].CrossRefGoogle Scholar
  9. [9]
    S. Hohenegger and I. Kirsch, A note on the holography of Chern-Simons matter theories with flavour, JHEP 04 (2009) 129 [arXiv:0903.1730] [SPIRES].CrossRefADSGoogle Scholar
  10. [10]
    D. Gaiotto and D.L. Jafferis, Notes on adding D6 branes wrapping RP 3 in AdS 4 × CP 3, arXiv:0903.2175 [SPIRES].
  11. [11]
    Y. Hikida, W. Li and T. Takayanagi, ABJM with flavors and FQHE, JHEP 07 (2009) 065 [arXiv:0903.2194] [SPIRES].CrossRefADSGoogle Scholar
  12. [12]
    D. Martelli and J. Sparks, AdS 4 /CFT 3 duals from M2-branes at hypersurface singularities and their deformations, JHEP 12 (2009) 017 [arXiv:0909.2036] [SPIRES].CrossRefGoogle Scholar
  13. [13]
    M. Van Raamsdonk, Comments on the Bagger-Lambert theory and multiple M2-branes, JHEP 05 (2008) 105 [arXiv:0803.3803] [SPIRES].CrossRefADSGoogle Scholar
  14. [14]
    S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace, or one thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [SPIRES].Google Scholar
  15. [15]
    M. Benna, I. Klebanov, T. Klose and M. Smedback, Superconformal Chern-Simons theories and AdS 4 /CFT 3 correspondence, JHEP 09 (2008) 072 [arXiv:0806.1519] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    L.V. Avdeev, G.V. Grigorev and D.I. Kazakov, Renormalizations in abelian Chern-Simons field theories with matter, Nucl. Phys. B 382 (1992) 561 [SPIRES].CrossRefADSGoogle Scholar
  17. [17]
    L.V. Avdeev, D.I. Kazakov and I.N. Kondrashuk, Renormalizations in supersymmetric and nonsupersymmetric non-abelian Chern-Simons field theories with matter, Nucl. Phys. B 391 (1993) 333 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    H.-C. Kao, K.-M. Lee and T. Lee, The Chern-Simons coefficient in supersymmetric Yang-Mills Chern-Simons theories, Phys. Lett. B 373 (1996) 94 [hep-th/9506170] [SPIRES].MathSciNetGoogle Scholar
  19. [19]
    M.S. Bianchi, S. Penati and M. Siani, in preparation.Google Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Marco S. Bianchi
    • 1
    • 2
  • Silvia Penati
    • 1
    • 2
  • Massimo Siani
    • 1
    • 2
  1. 1.Dipartimento di Fisica dell’Università degli studi di Milano-BicoccaMilanoItaly
  2. 2.INFN, Sezione di Milano-BicoccaMilanoItaly

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