Skip to main content
SpringerLink
Log in

Infrared stability of ABJ-like theories

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

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].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.H. Schwarz, Superconformal Chern-Simons theories, JHEP 11 (2004) 078 [hep-th/0411077] [SPIRES].

    Article  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  8. N. Akerblom, C. Sämann and M. Wolf, Marginal deformations and 3-algebra structures, Nucl. Phys. B 826 (2010) 456 [arXiv:0906.1705] [SPIRES].

    Article  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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. Y. Hikida, W. Li and T. Takayanagi, ABJM with flavors and FQHE, JHEP 07 (2009) 065 [arXiv:0903.2194] [SPIRES].

    Article  ADS  Google Scholar 

  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].

    Article  Google Scholar 

  13. M. Van Raamsdonk, Comments on the Bagger-Lambert theory and multiple M2-branes, JHEP 05 (2008) 105 [arXiv:0803.3803] [SPIRES].

    Article  ADS  Google Scholar 

  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. 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].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    MathSciNet  Google Scholar 

  19. M.S. Bianchi, S. Penati and M. Siani, in preparation.

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica dell’Università degli studi di Milano-Bicocca, Piazza della Scienza 3, I-20126, Milano, Italy

    Marco S. Bianchi, Silvia Penati & Massimo Siani

  2. INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126, Milano, Italy

    Marco S. Bianchi, Silvia Penati & Massimo Siani

Authors
  1. Marco S. Bianchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Silvia Penati
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Massimo Siani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marco S. Bianchi.

Additional information

ArXiv ePrint: 0910.5200

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bianchi, M.S., Penati, S. & Siani, M. Infrared stability of ABJ-like theories. J. High Energ. Phys. 2010, 80 (2010). https://doi.org/10.1007/JHEP01(2010)080

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP01(2010)080

Keywords

Search

Navigation