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The conformal manifold of Chern-Simons matter theories

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Abstract

We determine perturbatively the conformal manifold of \( \mathcal{N} = 2 \) Chern-Simons matter theories with the aim of checking in the three dimensional case the general prescription based on global symmetry breaking, recently introduced in [1–3]. We discuss in details few remarkable cases like the \( \mathcal{N} = 6 \) ABJM theory and its less supersymmetric generalizations with/without flavors. In all cases we find perfect agreement with the predictions of global symmetry breaking prescription. For unflavored theories the conformal manifold is a three dimensional compact surface. This feature is peculiar of three dimensions, as it has no direct analogue in four dimensional supersymmetric models.

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References

  1. D. Green, Z. Komargodski, N. Seiberg, Y. Tachikawa and B. Wecht, Exactly marginal deformations and global symmetries, JHEP 06 (2010) 106 [arXiv:1005.3546] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  2. B. Kol, On conformal deformations, JHEP 09 (2002) 046 [hep-th/0205141] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. B. Kol, On conformal deformations II, arXiv:1005.4408 [SPIRES].

  4. R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. 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 

  7. D. Gaiotto and E. Witten, Janus configurations, Chern-Simons couplings, and the Θ-angle in N = 4 super Yang-Mills theory, JHEP 06 (2010) 097 [arXiv:0804.2907] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  9. 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 

  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. K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N=4 superconformal Chern-Simons theories with hyper and twisted hyper multiplets, JHEP 07 (2008) 091 [arXiv:0805.3662] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. 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 

  14. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  16. K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N=5,6 superconformal Chern-Simons theories and M2-branes on orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. M. Schnabl and Y. Tachikawa, Classification of N = 6 superconformal theories of ABJM type, JHEP 09 (2010) 103 [arXiv:0807.1102] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  18. 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 

  19. 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 

  20. 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 

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

  22. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  24. 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 

  25. M. Fujita, W. Li, S. Ryu and T. Takayanagi, Fractional quantum hall effect via holography: Chern-Simons, edge states and hierarchy, JHEP 06 (2009) 066 [arXiv:0901.0924] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  26. 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 

  27. D. Gaiotto and D.L. Jafferis, Notes on adding D6 branes wrapping RP3 in AdS4 x CP3, arXiv:0903.2175 [SPIRES].

  28. 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 

  29. M. Fujita and T.-S. Tai, Eschenburg space as gravity dual of flavored N = 4 Chern-Simons-matter theory, JHEP 09 (2009) 062 [arXiv:0906.0253] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  30. F. Benini, C. Closset and S. Cremonesi, Chiral flavors and M2-branes at toric CY4 singularities, JHEP 02 (2010) 036 [arXiv:0911.4127] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  31. 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 

  32. 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 

  33. 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 

  34. 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  MathSciNet  Google Scholar 

  35. C.-M. Chang and X. Yin, Families of conformal fixed points of N = 2 Chern-Simons-Matter theories, JHEP 05 (2010) 108 [arXiv:1002.0568] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  36. 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 [Teor. Mat. Fiz. 77 (1988) 97] [SPIRES].

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Google Scholar 

  39. S.J. Gates, Jr. and H. Nishino, Remarks on the N = 2 supersymmetric Chern-Simons theories, Phys. Lett. B 281 (1992) 72 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  40. H. Nishino and S.J. Gates, Jr., Chern-Simons theories with supersymmetries in three-dimensions, Int. J. Mod. Phys. A 8 (1993) 3371 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  41. 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 

  42. 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 

  43. 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 

  44. 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 

  45. S. Benvenuti and A. Hanany, Conformal manifolds for the conifold and other toric field theories, JHEP 08 (2005) 024 [hep-th/0502043] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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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

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

    Marco S. Bianchi & Silvia Penati

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  1. Marco S. Bianchi
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  2. Silvia Penati
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Correspondence to Marco S. Bianchi.

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ArXiv ePrint: 1009.6223

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Bianchi, M.S., Penati, S. The conformal manifold of Chern-Simons matter theories. J. High Energ. Phys. 2011, 47 (2011). https://doi.org/10.1007/JHEP01(2011)047

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