Skip to main content
SpringerLink
Log in

On the infrared behaviour of 3d Chern-Simons theories in \( \mathcal{N} = 2 \) superspace

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

Abstract

We discuss the problem of infrared divergences in the \( \mathcal{N} = 2 \) superspace approach to classically marginal three-dimensional Chern-Simons-matter theories. Considering the specific case of ABJM theory, we describe the origin of such divergences and offer a prescription to eliminate them by introducing non-trivial gauge-fixing terms in the action. We also comment on the extension of our procedure to higher loop order and to general three-dimensional Chern-Simons-matter models.

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. R. Jackiw and S. Templeton, How Superrenormalizable Interactions Cure their Infrared Divergences, Phys. Rev. D 23 (1981) 2291 [SPIRES].

    ADS  Google Scholar 

  2. E.C. Poggio and H.R. Quinn, The Infrared Behavior of Zero-Mass Green’s Functions and the Absence of Quark Confinement in Perturbation Theory, Phys. Rev. D 14 (1976) 578 [SPIRES].

    ADS  Google Scholar 

  3. M.T. Grisaru, M. Roček and W. Siegel, SUperloops 3, Beta 0: A Calculation In N = 4 Yang-Mills Theory, Nucl. Phys. B 183 (1981) 141 [SPIRES].

    Article  ADS  Google Scholar 

  4. L.F. Abbott, M.T. Grisaru and D. Zanon, Infrared Divergences And A Nonlocal Gauge For Superspace Yang-Mills Theory, Nucl. Phys. B 244 (1984) 454 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  5. 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 

  6. 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 

  7. 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 

  8. 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 

  9. L.V. Avdeev, D.I. Kazakov and I.N. Kondrashuk, Renormalizations in supersymmetric and nonsupersymmetric nonAbelian Chern-Simons field theories with matter, Nucl. Phys. B 391 (1993) 333 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. N.K. Nielsen, GHost Counting In Supergravity, Nucl. Phys. B 140 (1978) 499 [SPIRES].

    Article  ADS  Google Scholar 

  11. R.E. Kallosh, Modified Feynman Rules in Supergravity, Nucl. Phys. B 141 (1978) 141 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. M.S. Bianchi, S. Penati and M. Siani, Infrared stability of ABJ-like theories, JHEP 01 (2010) 080 [arXiv:0910.5200] [SPIRES].

    Article  ADS  Google Scholar 

  13. M.S. Bianchi, S. Penati and M. Siani, Infrared Stability of N = 2 Chern-Simons Matter Theories, JHEP 05 (2010) 106 [arXiv:0912.4282] [SPIRES].

    Article  ADS  Google Scholar 

  14. N. Akerblom, C. Sämann and M. Wolf, Marginal Deformations and 3-Algebra Structures, Nucl. Phys. B 826 (2010) 456 [arXiv:0906.1705] [SPIRES].

    Article  ADS  Google Scholar 

  15. W. Chen, G.W. Semenoff and Y.-S. Wu, Two loop analysis of nonAbelian Chern-Simons theory, Phys. Rev. D 46 (1992) 5521 [hep-th/9209005] [SPIRES].

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  17. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  19. A. Mauri and A.C. Petkou, An N = 1 Superfield Action for M2 branes, Phys. Lett. B 666 (2008) 527 [arXiv:0806.2270] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  20. E.E. Boos and A.I. Davydychev, A Method of evaluating massive Feynman integrals, Theor. Math. Phys. 89 (1991) 1052 [Teor. Mat. Fiz. 89 (1991) 56] [SPIRES].

    Article  MathSciNet  Google Scholar 

  21. V.A. Smirnov, Evaluating Feynman Integrals, Springer Tracts Mod. Phys. 211 (2004) 1 [SPIRES].

    Google Scholar 

  22. I.L. Buchbinder, N.G. Pletnev and I.B. Samsonov, Effective action of three-dimensional extended supersymmetric matter on gauge superfield background, JHEP 04 (2010) 124 [arXiv:1003.4806] [SPIRES].

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  24. I.L. Buchbinder et al., Quantum N = 3, D = 3 Chern-Simons Matter Theories in Harmonic Superspace, JHEP 10 (2009) 075 [arXiv:0909.2970] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. P.C. West, A Comment on the nonrenormalization theorem in supersymmetric theories, Phys. Lett. B 258 (1991) 375 [SPIRES].

    ADS  Google Scholar 

  26. I. Jack, D.R.T. Jones and P.C. West, Not the no-renormalisation theorem?, Phys. Lett. B 258 (1991) 382 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  27. P.C. West, Quantum corrections in the supersymmetric effective superpotential and resulting modification of patterns of symmetry breaking, Phys. Lett. B 261 (1991) 396 [SPIRES].

    ADS  Google Scholar 

  28. R. Argurio, G. Ferretti and R. Heise, An introduction to supersymmetric gauge theories and matrix models, Int. J. Mod. Phys. A 19 (2004) 2015 [hep-th/0311066] [SPIRES].

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Via Celoria 16, I-20133, Milano, Italy

    Matías Leoni & Andrea Mauri

Authors
  1. Matías Leoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Mauri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrea Mauri.

Additional information

ArXiv ePrint: 1006.2341

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leoni, M., Mauri, A. On the infrared behaviour of 3d Chern-Simons theories in \( \mathcal{N} = 2 \) superspace. J. High Energ. Phys. 2010, 128 (2010). https://doi.org/10.1007/JHEP11(2010)128

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2010)128

Keywords

Search

Navigation