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Families of conformal fixed points of \( \mathcal{N} = 2 \) Chern-Simons-matter theories

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Abstract

We argue that a large class of \( \mathcal{N} = 2 \) Chern-Simons-matter theories in three dimensions have a continuous family of exact IR fixed points described by suitable quartic superpotentials, based on holomorphy. The entire family exists in the perturbative regime. A nontrivial check is performed by computing the 4-loop beta function of the quartic couplings, in the ’t Hooft limit, with a large number of flavors. We find that the 4-loop beta function can only deform the family of 2-loop fixed points, and does not change the dimension of this family. We further present an explicit computation of a perturbative correction to the Zamolodchikov metric on this space of three-dimensional superconformal field theories.

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References

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

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  3. 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 

  4. 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 

  5. 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 

  6. 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 

  7. A.N. Kapustin and P.I. Pronin, Nonrenormalization theorem for gauge coupling in (2 + 1)-dimensions, Mod. Phys. Lett. A 9 (1994) 1925 [hep-th/9401053] [SPIRES].

    ADS  Google Scholar 

  8. D. Gaiotto and E. Witten, Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N = 4 Super Yang-Mills Theory, arXiv:0804.2907 [SPIRES].

  9. 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 

  10. 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 

  11. 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 

  12. M.S. Bianchi, S. Penati and M. Siani, Infrared Stability of N = 2 Chern-Simons Matter Theories, arXiv:0912.4282 [SPIRES].

  13. N. Seiberg, Naturalness Versus Supersymmetric Non-renormalization Theorems, Phys. Lett. B 318 (1993) 469 [hep-ph/9309335] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  14. T. Hayashi, Y. Ohshima, K. Okuyama and H. Suzuki, Invariant regularization of supersymmetric chiral gauge theory, Prog. Theor. Phys. 100 (1998) 627 [hep-th/9801062] [SPIRES].

    Article  ADS  Google Scholar 

  15. E. Poppitz and L. Randall, Holomorphic anomalies and the nonrenormalization theorem, Phys. Lett. B 389 (1996) 280 [hep-th/9608157] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  16. N. Arkani-Hamed and H. Murayama, Holomorphy, rescaling anomalies and exact β-functions in supersymmetric gauge theories, JHEP 06 (2000) 030 [hep-th/9707133] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. S. Weinberg, Non-renormalization theorems in non-renormalizable theories, Phys. Rev. Lett. 80 (1998) 3702 [hep-th/9803099] [SPIRES].

    Article  ADS  Google Scholar 

  18. A.B. Zamolodchikov, Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory, JETP Lett. 43 (1986) 730 [Pisma Zh. Eksp. Teor. Fiz. 43 (1986) 565] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  19. D. Martelli and J. Sparks, Notes on toric Sasaki-Einstein seven-manifolds and AdS 4/CFT 3, JHEP 11 (2008) 016 [arXiv:0808.0904] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. 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 

  21. 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  MathSciNet  ADS  Google Scholar 

  22. 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 

  23. 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 

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Authors and Affiliations

  1. Jefferson Physical Laboratory, Harvard University, Cambridge, MA, 02138, U.S.A.

    Chi-Ming Chang & Xi Yin

  2. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.

    Xi Yin

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  1. Chi-Ming Chang
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  2. Xi Yin
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Correspondence to Chi-Ming Chang.

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ArXiv ePrint: 1002.0568

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Chang, CM., Yin, X. Families of conformal fixed points of \( \mathcal{N} = 2 \) Chern-Simons-matter theories. J. High Energ. Phys. 2010, 108 (2010). https://doi.org/10.1007/JHEP05(2010)108

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