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Perturbative search for dead-end CFTs

  • Yu NakayamaEmail author
Open Access
Article

Abstract

To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a. dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian description. In three dimensions, the only candidates are pure (Abelian) gauge theories, which may be further deformed by Chern-Simons terms. In four dimensions, we show that there are infinitely many non-trivial candidates based on chiral gauge theories. Using the three-loop beta functions, we compute the gap of scaling dimensions above the marginal value, and it can be as small as \( \mathcal{O}\left(1{0}^{-5}\right) \) and robust against the perturbative corrections. These classes of candidates are very weakly coupled and our perturbative conclusion seems difficult to refute. Thus, the hypothesis that non-trivial dead-end CFTs do not exist is likely to be false in four dimensions.

Keywords

Conformal and W Symmetry Renormalization Group 

Notes

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References

  1. [1]
    P. Bak, C. Tang and K. Wiesenfeld, Self-organized criticality: an explanation of 1/f noise, Phys. Rev. Lett. 59 (1987) 381 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    H.J. Jensen, Self-organized criticality, Cambridge University Press, Cambridge U.K. (1998).CrossRefzbMATHGoogle Scholar
  3. [3]
    Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J. Polchinski, Scale and conformal invariance in quantum field theory, Nucl. Phys. B 303 (1988) 226 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    M.A. Luty, J. Polchinski and R. Rattazzi, The a-theorem and the asymptotics of 4D quantum field theory, JHEP 01 (2013) 152 [arXiv:1204.5221] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Z. Komargodski and A. Zhiboedov, Convexity and liberation at large spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    Y. Nakayama, Scale invariance vs. conformal invariance, Phys. Rept. 569 (2015) 1 [arXiv:1302.0884] [INSPIRE].
  8. [8]
    C. Beem, L. Rastelli and B.C. van Rees, The \( \mathcal{N} \) = 4 superconformal bootstrap, Phys. Rev. Lett. 111 (2013) 071601 [arXiv:1304.1803] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    R. Jackiw and S.-Y. Pi, Tutorial on scale and conformal symmetries in diverse dimensions, J. Phys. A 44 (2011) 223001 [arXiv:1101.4886] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  10. [10]
    S. El-Showk, Y. Nakayama and S. Rychkov, What Maxwell theory in D <> 4 teaches us about scale and conformal invariance, Nucl. Phys. B 848 (2011) 578 [arXiv:1101.5385] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    M. Hermele, T. Senthil and M. Fisher Algebraic spin liquid as the mother of many competing orders, Phys. Rev. B 72 (2005) 104404 [Erratum ibid. 76 (2007) 149906] [cond-mat/0502215].
  12. [12]
    M. Hermele, Y. Ran, P. Lee and X.G. Wen, Properties of an algebraic spin liquid on the kagome lattice, Phys. Rev. B 77 (2008) 224413 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    M. Lüscher, Chiral gauge theories revisited, hep-th/0102028 [INSPIRE].
  14. [14]
    E. Poppitz and M. Ünsal, Conformality or confinement: (IR)relevance of topological excitations, JHEP 09 (2009) 050 [arXiv:0906.5156] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    W.E. Caswell, Asymptotic behavior of nonabelian gauge theories to two loop order, Phys. Rev. Lett. 33 (1974) 244 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    T. Banks and A. Zaks, On the phase structure of vector-like gauge theories with massless fermions, Nucl. Phys. B 196 (1982) 189 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    T. Appelquist, G.T. Fleming, M.F. Lin, E.T. Neil and D.A. Schaich, Lattice simulations and infrared conformality, Phys. Rev. D 84 (2011) 054501 [arXiv:1106.2148] [INSPIRE].ADSGoogle Scholar
  18. [18]
    T. DeGrand, Finite-size scaling tests for spectra in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions, Phys. Rev. D 84 (2011) 116901 [arXiv:1109.1237] [INSPIRE].ADSGoogle Scholar
  19. [19]
    Y. Aoki et al., Lattice study of conformality in twelve-flavor QCD, Phys. Rev. D 86 (2012) 054506 [arXiv:1207.3060] [INSPIRE].ADSGoogle Scholar
  20. [20]
    A. Cheng, A. Hasenfratz, G. Petropoulos and D. Schaich, Scale-dependent mass anomalous dimension from Dirac eigenmodes, JHEP 07 (2013) 061 [arXiv:1301.1355] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    K.-I. Ishikawa, Y. Iwasaki, Y. Nakayama and T. Yoshie, Global structure of conformal theories in the SU(3) gauge theory, Phys. Rev. D 89 (2014) 114503 [arXiv:1310.5049] [INSPIRE].ADSGoogle Scholar
  22. [22]
    H. Georgi and S.L. Glashow, Unity of all elementary particle forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    I. Bars and S. Yankielowicz, Composite quarks and leptons as solutions of anomaly constraints, Phys. Lett. B 101 (1981) 159 [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    M. Mojaza, Aspects of conformal gauge theories, Master Thesis, University of Southern Denmark, Denmark (2011).Google Scholar
  25. [25]
    G. Veneziano, U(1) without instantons, Nucl. Phys. B 159 (1979) 213 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    S. Hellerman, A universal inequality for CFT and quantum gravity, JHEP 08 (2011) 130 [arXiv:0902.2790] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    J.D. Qualls and A.D. Shapere, Bounds on operator dimensions in 2D conformal field theories, JHEP 05 (2014) 091 [arXiv:1312.0038] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    J.D. Qualls, Universal bounds in even-spin CFTs, arXiv:1412.0383 [INSPIRE].
  29. [29]
    E. Witten, Three-dimensional gravity revisited, arXiv:0706.3359 [INSPIRE].
  30. [30]
    I. Frenkel, J. Lepowsky and A. Meurman, Vertex operator algebras and the monster, Academic, Boston U.S.A. (1988).zbMATHGoogle Scholar
  31. [31]
    D. Poland, D. Simmons-Duffin and A. Vichi, Carving out the space of 4D CFTs, JHEP 05 (2012) 110 [arXiv:1109.5176] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    J. Polchinski and E. Silverstein, Dual purpose landscaping tools: small extra dimensions in AdS/CFT, arXiv:0908.0756 [INSPIRE].
  33. [33]
    S. de Alwis, R.K. Gupta, F. Quevedo and R. Valandro, On KKLT/CFT and LVS/CFT dualities, arXiv:1412.6999 [INSPIRE].
  34. [34]
    E. Kiritsis, Asymptotic freedom, asymptotic flatness and cosmology, JCAP 11 (2013) 011 [arXiv:1307.5873] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    L. Mihaila, Three-loop gauge beta function in non-simple gauge groups, PoS(RADCOR 2013)060.
  36. [36]
    A.G.M. Pickering, J.A. Gracey and D.R.T. Jones, Three loop gauge β-function for the most general single gauge coupling theory, Phys. Lett. B 510 (2001) 347 [Phys. Lett. B 512 (2001) 230] [Erratum ibid. B 535 (2002) 377] [hep-ph/0104247] [INSPIRE].

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© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Walter Burke Institute for Theoretical Physics, California Institute of TechnologyPasadenaU.S.A.

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