Skip to main content
SpringerLink
Log in

Infrared stability of \( \mathcal{N} = 2 \) Chern-Simons matter theories

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

Abstract

According to the AdS4/CFT3 correspondence, \( \mathcal{N} = 2 \) supersymmetric Chern-Simons matter theories should have a stable fixed point in the infrared. In order to support this prediction we study RG flows of two-level Chern-Simons matter theories with/without flavors induced by the most general marginal superpotential compatible with \( \mathcal{N} = 2 \) supersymmetry. At two loops we determine the complete spectrum of fixed points and study their IR stability. Our analysis covers a large class of models including perturbations of the ABJM/ABJ theories with and without flavors, \( \mathcal{N} = 2,3 \) theories with different CS levels corresponding to turning on a Romans mass and β-deformations. In all cases we find curves (or surfaces) of fixed points which are globally IR stable. Each fixed point has only one direction of stability which in the ABJM case coincides with the maximal global symmetry preserving perturbation, whereas along any other direction the system flows to a different fixed point on the surface. The motion within the surface is driven by perturbations which are exactly marginal. The question of conformal invariance vs. finiteness is also addressed: While in general vanishing beta-functions imply two-loop finiteness, we find a particular set of flavored theories where this is no longer true.

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. A.S. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978) 247 [SPIRES].

    Article  MATH  ADS  Google Scholar 

  2. E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989) 351 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-matter theories, JHEP 08 (2007) 056 [arXiv:0704.3740] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  5. D. Gaiotto and E. Witten, Janus configurations, Chern-Simons couplings, and the θ-angle in N = 4 super Yang-Mills theory, arXiv:0804.2907 [SPIRES].

  6. H.-C. Kao and K.-M. Lee, Selfdual Chern-Simons systems with an N = 3 extended supersymmetry, Phys. Rev. D 46 (1992) 4691 [hep-th/9205115] [SPIRES].

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  8. 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 

  9. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  11. 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 

  12. 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].

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

    Article  MathSciNet  ADS  Google Scholar 

  14. T. Nishioka and T. Takayanagi, On type IIA Penrose limit and N = 6 Chern-Simons theories, JHEP 08 (2008) 001 [arXiv:0806.3391] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. J.A. Minahan and K. Zarembo, The Bethe ansatz for superconformal Chern-Simons, JHEP 09 (2008) 040 [arXiv:0806.3951] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. J.A. Minahan, W. Schulgin and K. Zarembo, Two loop integrability for Chern-Simons theories with N = 6 supersymmetry, JHEP 03 (2009) 057 [arXiv:0901.1142] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. D. Gaiotto, S. Giombi and X. Yin, Spin chains in N = 6 superconformal Chern-Simons-matter theory, JHEP 04 (2009) 066 [arXiv:0806.4589] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. D. Bak and S.-J. Rey, Integrable spin chain in superconformal Chern-Simons theory, JHEP 10 (2008) 053 [arXiv:0807.2063] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. N. Gromov and P. Vieira, The all loop AdS 4/CFT 3 Bethe ansatz, JHEP 01 (2009) 016 [arXiv:0807.0777] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. D. Bak, D. Gang and S.-J. Rey, Integrable spin chain of superconformal U(M) × U(N) Chern-Simons theory, JHEP 10 (2008) 038 [arXiv:0808.0170] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  21. C. Kristjansen, M. Orselli and K. Zoubos, Non-planar ABJM theory and integrability, JHEP 03 (2009) 037 [arXiv:0811.2150] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. N. Gromov, V. Kazakov and P. Vieira, Exact spectrum of anomalous dimensions of planar N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 103 (2009) 131601 [arXiv:0901.3753] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. B.I. Zwiebel, Two-loop integrability of planar N = 6 superconformal Chern-Simons theory, J. Phys. A 42 (2009) 495402 [arXiv:0901.0411] [SPIRES].

    MathSciNet  Google Scholar 

  24. D. Bak, H. Min and S.-J. Rey, Integrability of N = 6 Chern-Simons theory at six loops and beyond, arXiv:0911.0689 [SPIRES].

  25. D. Berenstein and D. Trancanelli, Three-dimensional N = 6 SCFT’s and their membrane dynamics, Phys. Rev. D 78 (2008) 106009 [arXiv:0808.2503] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  26. K. Hosomichi et al., A nonperturbative test of M2-brane theory, JHEP 11 (2008) 058 [arXiv:0809.1771] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  27. S. Kim, The complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [arXiv:0903.4172] [SPIRES].

    Article  ADS  Google Scholar 

  28. M.M. Sheikh-Jabbari and J. Simon, On half-BPS states of the ABJM theory, JHEP 08 (2009) 073 [arXiv:0904.4605] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. M.K. Benna, I.R. Klebanov and T. Klose, Charges of monopole operators in Chern-Simons Yang-Mills theory, JHEP 01 (2010) 110 [arXiv:0906.3008] [SPIRES].

    Article  Google Scholar 

  30. D. Berenstein and J. Park, The BPS spectrum of monopole operators in ABJM: towards a field theory description of the giant torus, arXiv:0906.3817 [SPIRES].

  31. S. Kim and K. Madhu, Aspects of monopole operators in N = 6 Chern-Simons theory, JHEP 12 (2009) 018 [arXiv:0906.4751] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. A. Giveon, D. Kutasov and O. Lunin, Spontaneous SUSY breaking in various dimensions, Nucl. Phys. B 822 (2009) 127 [arXiv:0904.2175] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  33. A. Amariti and M. Siani, R-symmetry and supersymmetry breaking in 3D WZ models, JHEP 08 (2009) 055 [arXiv:0905.4725] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  35. M. Schnabl and Y. Tachikawa, Classification of N = 6 superconformal theories of ABJM type, arXiv:0807.1102 [SPIRES].

  36. 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 

  37. D. Martelli and J. Sparks, Moduli spaces of Chern-Simons quiver gauge theories and AdS 4/CFT 3, Phys. Rev. D 78 (2008) 126005 [arXiv:0808.0912] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  38. A. Hanany and A. Zaffaroni, Tilings, Chern-Simons theories and M2 branes, JHEP 10 (2008) 111 [arXiv:0808.1244] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  39. S. Franco, A. Hanany, J. Park and D. Rodriguez-Gomez, Towards M2-brane theories for generic toric singularities, JHEP 12 (2008) 110 [arXiv:0809.3237] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  40. A. Hanany and Y.-H. He, M2-branes and quiver Chern-Simons: a taxonomic study, arXiv:0811.4044 [SPIRES].

  41. E. Imeroni, On deformed gauge theories and their string/M-theory duals, JHEP 10 (2008) 026 [arXiv:0808.1271] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  42. D.L. Jafferis and A. Tomasiello, A simple class of N = 3 gauge/gravity duals, JHEP 10 (2008) 101 [arXiv:0808.0864] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  43. D. Gaiotto and A. Tomasiello, The gauge dual of Romans mass, JHEP 01 (2010) 015 [arXiv:0901.0969] [SPIRES].

    Article  Google Scholar 

  44. D. Gaiotto and A. Tomasiello, Perturbing gauge/gravity duals by a Romans mass, J. Phys. A 42 (2009) 465205 [arXiv:0904.3959] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  45. 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  ADS  Google Scholar 

  46. 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 

  47. D. Gaiotto and D.L. Jafferis, Notes on adding D6 branes wrapping RP3 in AdS4 × CP 3, arXiv:0903.2175 [SPIRES].

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

    Article  MathSciNet  ADS  Google Scholar 

  49. F. Benini, C. Closset and S. Cremonesi, Chiral flavors and M2-branes at toric CY 4 singularities, JHEP 02 (2010) 036 [arXiv:0911.4127] [SPIRES].

    Article  Google Scholar 

  50. D.L. Jafferis, Quantum corrections to N = 2 Chern-Simons theories with flavor and their AdS 4 duals, arXiv:0911.4324 [SPIRES].

  51. L.J. Romans, Massive N = 2a supergravity in ten-dimensions, Phys. Lett. B 169 (1986) 374 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  52. P. de Medeiros, J. Figueroa-O’Farrill, E. Méndez-Escobar and P. Ritter, On the Lie-algebraic origin of metric 3-algebras, Commun. Math. Phys. 290 (2009) 871 [arXiv:0809.1086] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  53. P. de Medeiros, J. Figueroa-O’Farrill and E. Méndez-Escobar, Superpotentials for superconformal Chern-Simons theories from representation theory, J. Phys. A 42 (2009) 485204 [arXiv:0908.2125] [SPIRES].

    Google Scholar 

  54. B.E.W. Nilsson and C.N. Pope, Hopf fibration of eleven-dimensional supergravity, Class. Quant. Grav. 1 (1984) 499 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  Google Scholar 

  56. B.M. Zupnik and D.G. Pak, Superfield formulation of the simplest three-dimensional gauge theories and conformal supergravities, Theor. Math. Phys. 77 (1988) 1070 [SPIRES].

    Article  MathSciNet  Google Scholar 

  57. B.M. Zupnik and D.G. Pak, Topologically massive gauge theories in superspace, Sov. Phys. J. 31 (1988) 962 [SPIRES].

    Article  Google Scholar 

  58. E.A. Ivanov, Chern-Simons matter systems with manifest N = 2 supersymmetry, Phys. Lett. B 268 (1991) 203 [SPIRES].

    ADS  Google Scholar 

  59. 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 

  60. 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 

  61. 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 

  62. 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 

  63. M.T. Grisaru, W. Siegel and M. Roček, Improved methods for supergraphs, Nucl. Phys. B 159 (1979) 429 [SPIRES].

    Article  ADS  Google Scholar 

  64. 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 

  65. A. Mauri, S. Penati, A. Santambrogio and D. Zanon, Exact results in planar N = 1 superconformal Yang-Mills theory, JHEP 11 (2005) 024 [hep-th/0507282] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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 Massimo Siani.

Additional information

ArXiv ePrint: 0912.4282

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bianchi, M.S., Penati, S. & Siani, M. Infrared stability of \( \mathcal{N} = 2 \) Chern-Simons matter theories. J. High Energ. Phys. 2010, 106 (2010). https://doi.org/10.1007/JHEP05(2010)106

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2010)106

Keywords

Search

Navigation