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Journal of High Energy Physics

, 2018:58 | Cite as

Flows, fixed points and duality in Chern-Simons-matter theories

  • Ofer Aharony
  • Sachin JainEmail author
  • Shiraz Minwalla
Open Access
Regular Article - Theoretical Physics

Abstract

It has been conjectured that 3d fermions minimally coupled to Chern-Simons gauge fields are dual to 3d critical scalars, also minimally coupled to Chern-Simons gauge fields. The large N arguments for this duality can formally be used to show that Chern-Simons-gauged critical (Gross-Neveu) fermions are also dual to gauged ‘regular ’ scalars at every order in a 1/N expansion, provided both theories are well-defined (when one fine-tunes the two relevant parameters of each of these theories to zero). In the strict large N limit these ‘quasi-bosonic’ theories appear as fixed lines parameterized by x6, the coefficient of a sextic term in the potential. While x6 is an exactly marginal deformation at leading order in large N, it develops a non-trivial β function at first subleading order in 1/N. We demonstrate that the beta function is a cubic polynomial in x6 at this order in 1/N, and compute the coefficients of the cubic and quadratic terms as a function of the ’t Hooft coupling. We conjecture that flows governed by this leading large N beta function have three fixed points for x6 at every non-zero value of the ’t Hooft coupling, implying the existence of three distinct regular bosonic and three distinct dual critical fermionic conformal fixed points, at every value of the ’t Hooft coupling. We analyze the phase structure of these fixed point theories at zero temperature. We also construct dual pairs of large N fine-tuned renormalization group flows from supersymmetric \( \mathcal{N}=2 \) Chern-Simons-matter theories, such that one of the flows ends up in the IR at a regular boson theory while its dual partner flows to a critical fermion theory. This construction suggests that the duality between these theories persists at finite N, at least when N is large.

Keywords

1/N Expansion Chern-Simons Theories Duality in Gauge Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B 644 (2002) 303 [Erratum ibid. B 660 (2003) 403] [hep-th/0205131] [INSPIRE].
  3. [3]
    S. Giombi and X. Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    S. Giombi, S. Minwalla, S. Prakash, S.P. Trivedi, S.R. Wadia and X. Yin, Chern-Simons Theory with Vector Fermion Matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
  5. [5]
    C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ Triality: from Higher Spin Fields to Strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [INSPIRE].
  6. [6]
    S. Giombi, Higher Spin — CFT Duality, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (TASI 2015), Boulder, CO, U.S.A., June 1-26, 2015, pp. 137-214 (2017) [DOI: https://doi.org/10.1142/9789813149441_0003] [arXiv:1607.02967] [INSPIRE].
  7. [7]
    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] [INSPIRE].
  8. [8]
    J. Maldacena and A. Zhiboedov, Constraining Conformal Field Theories with A Higher Spin Symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
  9. [9]
    J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].
  10. [10]
    D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-Matter theories, JHEP 08 (2007) 056 [arXiv:0704.3740] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities, JHEP 10 (2011) 075 [arXiv:1108.5373] [INSPIRE].
  12. [12]
    J. Park and K.-J. Park, Seiberg-like Dualities for 3d N = 2 Theories with SU(N) gauge group, JHEP 10 (2013) 198 [arXiv:1305.6280] [INSPIRE].
  13. [13]
    O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
  14. [14]
    A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].
  15. [15]
    S. Jain, S. Minwalla and S. Yokoyama, Chern Simons duality with a fundamental boson and fermion, JHEP 11 (2013) 037 [arXiv:1305.7235] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    K. Inbasekar, S. Jain, S. Mazumdar, S. Minwalla, V. Umesh and S. Yokoyama, Unitarity, crossing symmetry and duality in the scattering of \( \mathcal{N}=1 \) SUSY matter Chern-Simons theories, JHEP 10 (2015) 176 [arXiv:1505.06571] [INSPIRE].
  17. [17]
    G. Gur-Ari and R. Yacoby, Three Dimensional Bosonization From Supersymmetry, JHEP 11 (2015) 013 [arXiv:1507.04378] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    A. Kapustin, B. Willett and I. Yaakov, Tests of Seiberg-like Duality in Three Dimensions, arXiv:1012.4021 [INSPIRE].
  19. [19]
    B. Willett and I. Yaakov, N = 2 Dualities and Z Extremization in Three Dimensions, arXiv:1104.0487 [INSPIRE].
  20. [20]
    A. Kapustin, Seiberg-like duality in three dimensions for orthogonal gauge groups, arXiv:1104.0466 [INSPIRE].
  21. [21]
    K. Intriligator and N. Seiberg, Aspects of 3d N = 2 Chern-Simons-Matter Theories, JHEP 07 (2013) 079 [arXiv:1305.1633] [INSPIRE].
  22. [22]
    O. Aharony, G. Gur-Ari and R. Yacoby, d = 3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
  23. [23]
    D. Gaiotto, Z. Komargodski and N. Seiberg, Time-reversal breaking in QCD 4 , walls and dualities in 2 + 1 dimensions, JHEP 01 (2018) 110 [arXiv:1708.06806] [INSPIRE].
  24. [24]
    J. Gomis, Z. Komargodski and N. Seiberg, Phases Of Adjoint QCD 3 And Dualities, SciPost Phys. 5 (2018) 007 [arXiv:1710.03258] [INSPIRE].
  25. [25]
    D. Radičević, Disorder Operators in Chern-Simons-Fermion Theories, JHEP 03 (2016) 131 [arXiv:1511.01902] [INSPIRE].ADSzbMATHGoogle Scholar
  26. [26]
    O. Aharony, Baryons, monopoles and dualities in Chern-Simons-matter theories, JHEP 02 (2016) 093 [arXiv:1512.00161] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    O. Aharony, G. Gur-Ari and R. Yacoby, Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions, JHEP 12 (2012) 028 [arXiv:1207.4593] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    N. Seiberg, T. Senthil, C. Wang and E. Witten, A Duality Web in 2+1 Dimensions and Condensed Matter Physics, Annals Phys. 374 (2016) 395 [arXiv:1606.01989] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    G. Gur-Ari and R. Yacoby, Correlators of Large N Fermionic Chern-Simons Vector Models, JHEP 02 (2013) 150 [arXiv:1211.1866] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    A. Bedhotiya and S. Prakash, A test of bosonization at the level of four-point functions in Chern-Simons vector models, JHEP 12 (2015) 032 [arXiv:1506.05412] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  31. [31]
    S. Jain, M. Mandlik, S. Minwalla, T. Takimi, S.R. Wadia and S. Yokoyama, Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter, JHEP 04 (2015) 129 [arXiv:1404.6373] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  32. [32]
    Y. Dandekar, M. Mandlik and S. Minwalla, Poles in the S-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics, JHEP 04 (2015) 102 [arXiv:1407.1322] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    S. Yokoyama, Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models, JHEP 09 (2016) 105 [arXiv:1604.01897] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    S. Jain, S.P. Trivedi, S.R. Wadia and S. Yokoyama, Supersymmetric Chern-Simons Theories with Vector Matter, JHEP 10 (2012) 194 [arXiv:1207.4750] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    O. Aharony, S. Giombi, G. Gur-Ari, J. Maldacena and R. Yacoby, The Thermal Free Energy in Large N Chern-Simons-Matter Theories, JHEP 03 (2013) 121 [arXiv:1211.4843] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    S. Jain, S. Minwalla, T. Sharma, T. Takimi, S.R. Wadia and S. Yokoyama, Phases of large N vector Chern-Simons theories on S 2 × S 1, JHEP 09 (2013) 009 [arXiv:1301.6169] [INSPIRE].
  37. [37]
    T. Takimi, Duality and higher temperature phases of large N Chern-Simons matter theories on S 2 × S 1, JHEP 07 (2013) 177 [arXiv:1304.3725] [INSPIRE].
  38. [38]
    S. Yokoyama, A Note on Large N Thermal Free Energy in Supersymmetric Chern-Simons Vector Models, JHEP 01 (2014) 148 [arXiv:1310.0902] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  39. [39]
    S. Yokoyama, Chern-Simons-Fermion Vector Model with Chemical Potential, JHEP 01 (2013) 052 [arXiv:1210.4109] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].
  41. [41]
    R.D. Pisarski, Fixed point structure of \( \phi \) 6 in three-dimensions AT Large N , Phys. Rev. Lett. 48 (1982) 574 [INSPIRE].
  42. [42]
    E. Pomoni and L. Rastelli, Large N Field Theory and AdS Tachyons, JHEP 04 (2009) 020 [arXiv:0805.2261] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    R. Yacoby, Scalar Correlators in Bosonic Chern-Simons Vector Models, arXiv:1805.11627 [INSPIRE].
  44. [44]
    S. Minwalla and S. Yokoyama, Chern Simons Bosonization along RG Flows, JHEP 02 (2016) 103 [arXiv:1507.04546] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    A. Dey, I. Halder, S. Jain, L. Janagal, S. Minwalla and N. Prabhakar, Regular Boson Critical Fermion Chern-Simons dualities in the Higgsed Phase, to appear.Google Scholar
  46. [46]
    P.-S. Hsin and N. Seiberg, Level/rank Duality and Chern-Simons-Matter Theories, JHEP 09 (2016) 095 [arXiv:1607.07457] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    W. Siegel, Supersymmetric Dimensional Regularization via Dimensional Reduction, Phys. Lett. B 84 (1979) 193 [INSPIRE].
  48. [48]
    A.N. Vasiliev, Yu.M. Pismak and Yu.R. Khonkonen, 1/N Expansion: calculation of the exponent η in the order 1/N 3 by the conformal bootstrap method, Theor. Math. Phys. 50 (1982) 127 [INSPIRE].
  49. [49]
    A. Bzowski, P. McFadden and K. Skenderis, Implications of conformal invariance in momentum space, JHEP 03 (2014) 111 [arXiv:1304.7760] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    G.J. Turiaci and A. Zhiboedov, Veneziano Amplitude of Vasiliev Theory, JHEP 10 (2018) 034 [arXiv:1802.04390] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  51. [51]
    O. Aharony, L.F. Alday, A. Bissi and R. Yacoby, The Analytic Bootstrap for Large N Chern-Simons Vector Models, JHEP 08 (2018) 166 [arXiv:1805.04377] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  52. [52]
    S. Giombi, V. Gurucharan, V. Kirilin, S. Prakash and E. Skvortsov, On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models, JHEP 01 (2017) 058 [arXiv:1610.08472] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    O. Aharony, F. Benini, P.-S. Hsin and N. Seiberg, Chern-Simons-matter dualities with SO and USp gauge groups, JHEP 02 (2017) 072 [arXiv:1611.07874] [INSPIRE].
  54. [54]
    S. Choudhury et al., Bose-Fermi Chern-Simons Dualities in the Higgsed Phase, JHEP 11 (2018) 177 [arXiv:1804.08635] [INSPIRE].
  55. [55]
    S. Giombi, V. Kirilin and E. Skvortsov, Notes on Spinning Operators in Fermionic CFT, JHEP 05 (2017) 041 [arXiv:1701.06997] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. [56]
    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 [INSPIRE].
  57. [57]
    F. Benini, Three-dimensional dualities with bosons and fermions, JHEP 02 (2018) 068 [arXiv:1712.00020] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  58. [58]
    K. Jensen, A master bosonization duality, JHEP 01 (2018) 031 [arXiv:1712.04933] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  59. [59]
    E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
  60. [60]
    S. Grozdanov, Wilsonian Renormalisation and the Exact Cut-Off Scale from Holographic Duality, JHEP 06 (2012) 079 [arXiv:1112.3356] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    D. Das, S.R. Das and G. Mandal, Double Trace Flows and Holographic RG in dS/CFT correspondence, JHEP 11 (2013) 186 [arXiv:1306.0336] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    O. Aharony, G. Gur-Ari and N. Klinghoffer, The Holographic Dictionary for β-functions of Multi-trace Coupling Constants, JHEP 05 (2015) 031 [arXiv:1501.06664] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  63. [63]
    A. Kapustin and B. Willett, Wilson loops in supersymmetric Chern-Simons-matter theories and duality, arXiv:1302.2164 [INSPIRE].
  64. [64]
    O. Aharony and D. Fleischer, IR Dualities in General 3d Supersymmetric SU(N ) QCD Theories, JHEP 02 (2015) 162 [arXiv:1411.5475] [INSPIRE].
  65. [65]
    S.G. Naculich, H.A. Riggs and H.J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory, Phys. Lett. B 246 (1990) 417 [INSPIRE].
  66. [66]
    M. Camperi, F. Levstein and G. Zemba, The Large N Limit of Chern-Simons Gauge Theory, Phys. Lett. B 247 (1990) 549 [INSPIRE].
  67. [67]
    T. Nakanishi and A. Tsuchiya, Level rank duality of WZW models in conformal field theory, Commun. Math. Phys. 144 (1992) 351 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  68. [68]
    S.G. Naculich and H.J. Schnitzer, Level-rank duality of the U(N) WZW model, Chern-Simons theory and 2-D qYM theory, JHEP 06 (2007) 023 [hep-th/0703089] [INSPIRE].

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Particle Physics and AstrophysicsWeizmann Institute of ScienceRehovotIsrael
  2. 2.Indian Institute of Science Education and ResearchPuneIndia
  3. 3.Department of Theoretical Physics, Tata Institute of Fundamental ResearchMumbaiIndia

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