Skip to main content
SpringerLink
Log in

Improved bounds for CFT’s with global symmetries

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

Abstract

The four point functions of Conformal Field Theories (CFT’s) with global symmetries give rise to multiple crossing symmetry constraints. We explicitly study the correlator of four scalar operators transforming in the fundamental representation of a global SO(N) and the correlator of chiral and anti-chiral superfields in a superconformal field theory. In both cases the constraints take the form of a triple sum rule, whose feasibility can be translated into restrictions on the CFT spectrum and interactions. In the case of SO(N) global symmetry we derive bounds for the first scalar singlet operator entering the Operator Product Expansion (OPE) of two fundamental representations for different value of N. Bounds for the first scalar traceless-symmetric representation of the global symmetry are computed as well. Results for superconformal field theories improve previous investigations due to the use of the full set of constraints. Our analysis only assumes unitarity of the CFT, crossing symmetry of the four point function and existence of an OPE for scalars.

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. Belavin, A.M. Polyakov and A. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. A. Polyakov, Nonhamiltonian approach to conformal quantum field theory, Zh. Eksp. Teor. Fiz. 66 (1974) 23 [INSPIRE].

    MathSciNet  Google Scholar 

  3. T. Banks and A. Zaks, On the phase structure of vector-like gauge theories with massless fermions, Nucl. Phys. B 196 (1982) 189 [INSPIRE].

    Article  ADS  Google Scholar 

  4. A. Belavin and A. Migdal, Calculation of anomalous dimensions in non-abelian gauge field theories, Pisma Zh. Eksp. Teor. Fiz. 19 (1974) 317 [JETP Letters 19 (1974) 181] [INSPIRE].

    Google Scholar 

  5. N. Seiberg, Electric-magnetic duality in supersymmetric nonabelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4 d CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. F. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. F. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. V.S. Rychkov and A. Vichi, Universal constraints on conformal operator dimensions, Phys. Rev. D 80 (2009) 045006 [arXiv:0905.2211] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  11. F. Caracciolo and V.S. Rychkov, Rigorous limits on the interaction strength in quantum field theory, Phys. Rev. D 81 (2010) 085037 [arXiv:0912.2726] [INSPIRE].

    ADS  Google Scholar 

  12. R. Rattazzi, S. Rychkov and A. Vichi, Central charge bounds in 4 d conformal field theory, Phys. Rev. D 83 (2011) 046011 [arXiv:1009.2725] [INSPIRE].

    ADS  Google Scholar 

  13. D. Poland and D. Simmons-Duffin, Bounds on 4 d conformal and superconformal field theories, JHEP 05 (2011) 017 [arXiv:1009.2087] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. R. Rattazzi, S. Rychkov and A. Vichi, Bounds in 4 d conformal field theories with global symmetry, J. Phys. A 44 (2011) 035402 [arXiv:1009.5985] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  15. M.A. Luty and T. Okui, Conformal technicolor, JHEP 09 (2006) 070 [hep-ph/0409274] [INSPIRE].

    Article  ADS  Google Scholar 

  16. M.A. Luty, Strong conformal dynamics at the LHC and on the lattice, JHEP 04 (2009) 050 [arXiv:0806.1235] [INSPIRE].

    Article  ADS  Google Scholar 

  17. J. Galloway, J.A. Evans, M.A. Luty and R.A. Tacchi, Minimal conformal technicolor and precision electroweak tests, JHEP 10 (2010) 086 [arXiv:1001.1361] [INSPIRE].

    Google Scholar 

  18. V. Dobrev and V. Petkova, All positive energy unitary irreducible representations of extended conformal supersymmetry, Phys. Lett. B 162 (1985) 127 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  19. H. Osborn, N = 1 superconformal symmetry in four-dimensional quantum field theory, Annals Phys. 272 (1999) 243 [hep-th/9808041] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. F. Dolan and H. Osborn, Implications of N = 1 superconformal symmetry for chiral fields, Nucl. Phys. B 593 (2001) 599 [hep-th/0006098] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. J.-F. Fortin, K. Intriligator and A. Stergiou, Current OPEs in superconformal theories, JHEP 09 (2011) 071 [arXiv:1107.1721] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. S. Ferrara, R. Gatto and A. Grillo, Positivity restrictions on anomalous dimensions, Phys. Rev. D 9 (1974) 3564 [INSPIRE].

    ADS  Google Scholar 

  23. G. Mack, All unitary ray representations of the conformal group SU(2, 2) with positive energy, Commun. Math. Phys. 55 (1977) 1 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. D. Poland, D. Simmons-Duffin and A. Vichi, Carving out the space of 4d CFTs, arXiv:1109.5176 [INSPIRE].

Download references

Author information

Authors and Affiliations

  1. Institut de Théorie des Phénomènes Physiques, EPFL, CH-1015, Lausanne, Switzerland

    Alessandro Vichi

Authors
  1. Alessandro Vichi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alessandro Vichi.

Additional information

ArXiv ePrint: 1106.4037

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vichi, A. Improved bounds for CFT’s with global symmetries. J. High Energ. Phys. 2012, 162 (2012). https://doi.org/10.1007/JHEP01(2012)162

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP01(2012)162

Keywords

Search

Navigation