Skip to main content
SpringerLink
Log in

Superconformal flavor simplified

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

Abstract

A simple explanation of the flavor hierarchies can arise if matter fields interact with a conformal sector and different generations have different anomalous dimensions under the CFT. However, in the original study by Nelson and Strassler many supersymmetric models of this type were considered to be ‘incalculable’ because the R-charges were not sufficiently constrained by the superpotential. We point out that nearly all such models are calculable with the use of a-maximization. Utilizing this, we construct the simplest vector-like flavor models and discuss their viability. A significant constraint on these models comes from requiring that the visible gauge couplings remain perturbative throughout the conformal window needed to generate the hierarchies. However, we find that there is a small class of simple flavor models that can evade this bound.

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. C.D. Froggatt and H.B. Nielsen, Hierarchy of Quark Masses, Cabibbo Angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [SPIRES].

    Article  ADS  Google Scholar 

  2. M. Leurer, Y. Nir and N. Seiberg, Mass matrix models, Nucl. Phys. B 398 (1993) 319 [hep-ph/9212278] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. M. Leurer, Y. Nir and N. Seiberg, Mass matrix models: The Sequel, Nucl. Phys. B 420 (1994) 468 [hep-ph/9310320] [SPIRES].

    Article  ADS  Google Scholar 

  4. Y. Grossman and Y. Nir, Lepton mass matrix models, Nucl. Phys. B 448 (1995) 30 [hep-ph/9502418] [SPIRES].

    Article  ADS  Google Scholar 

  5. H. Georgi, A.E. Nelson and A. Manohar, On the proposition that all fermions are created equal, Phys. Lett. B 126 (1983) 169 [SPIRES].

    ADS  Google Scholar 

  6. A.E. Nelson and M.J. Strassler, Suppressing flavor anarchy, JHEP 09 (2000) 030 [hep-ph/0006251] [SPIRES].

    Article  ADS  Google Scholar 

  7. L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. T. Gherghetta and A. Pomarol, Bulk fields and supersymmetry in a slice of AdS, Nucl. Phys. B 586 (2000) 141 [hep-ph/0003129] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. S.J. Huber and Q. Shafi, Fermion Masses, Mixings and Proton Decay in a Randall-Sundrum Model, Phys. Lett. B 498 (2001) 256 [hep-ph/0010195] [SPIRES].

    ADS  Google Scholar 

  10. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].

    MATH  MathSciNet  ADS  Google Scholar 

  11. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  12. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].

    MATH  MathSciNet  Google Scholar 

  13. N. Arkani-Hamed, M. Porrati and L. Randall, Holography and phenomenology, JHEP 08 (2001) 017 [hep-th/0012148] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. R. Rattazzi and A. Zaffaroni, Comments on the holographic picture of the Randall-Sundrum model, JHEP 04 (2001) 021 [hep-th/0012248] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. K.A. Intriligator and B. Wecht, The exact superconformal R-symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. Particle Data Group collaboration, C. Amsler et al., Review of particle physics, Phys. Lett. B 667 (2008) 1 [SPIRES].

    ADS  Google Scholar 

  17. M.C. Gonzalez-Garcia, Neutrino Physics, Nucl. Phys. A 827 (2009) 5c–14c [arXiv:0901.2505] [SPIRES].

    ADS  Google Scholar 

  18. S. Antusch and M. Spinrath, Quark and lepton masses at the GUT scale including SUSY threshold corrections, Phys. Rev. D 78 (2008) 075020 [arXiv:0804.0717] [SPIRES].

    ADS  Google Scholar 

  19. J.L. Diaz-Cruz, H. Murayama and A. Pierce, Can supersymmetric loops correct the fermion mass relations in SU(5)?, Phys. Rev. D 65 (2002) 075011 [hep-ph/0012275] [SPIRES].

    ADS  Google Scholar 

  20. T. Ibrahim and P. Nath, SUSY QCD and SUSY electroweak loop corrections to b, t and τ masses including the effects of CP phases, Phys. Rev. D 67 (2003) 095003 [Erratum ibid. D 68 (2003) 019901] [hep-ph/0301110] [SPIRES].

    ADS  Google Scholar 

  21. J. Ferrandis and N. Haba, Supersymmetry breaking as the origin of flavor, Phys. Rev. D 70 (2004) 055003 [hep-ph/0404077] [SPIRES].

    ADS  Google Scholar 

  22. J.L. Diaz-Cruz, M. Gomez-Bock, R. Noriega-Papaqui and A. Rosado, A Numerical Analysis of the Supersymmetric Flavor Problem and Radiative Fermion Masses, Rev. Mex. Fis. 55 (2009) 270 [hep-ph/0512168] [SPIRES].

    Google Scholar 

  23. G. Ross and M. Serna, Unification and Fermion Mass Structure, Phys. Lett. B 664 (2008) 97 [arXiv:0704.1248] [SPIRES].

    ADS  Google Scholar 

  24. C.M. Maekawa and M.C. Rodriguez, Radiative Mechanism to Light Fermion Masses in the MSSM, JHEP 01 (2008) 072 [arXiv:0710.4943] [SPIRES].

    Article  ADS  Google Scholar 

  25. T. Enkhbat, SU(5) unification for Yukawas through SUSY threshold effects, arXiv:0909.5597 [SPIRES].

  26. M. Dine and W. Fischler, A Phenomenological Model of Particle Physics Based on Supersymmetry, Phys. Lett. B 110 (1982) 227 [SPIRES].

    ADS  Google Scholar 

  27. M. Dine and W. Fischler, A Supersymmetric GUT, Nucl. Phys. B 204 (1982) 346 [SPIRES].

    Article  ADS  Google Scholar 

  28. L. Álvarez-Gaumé, M. Claudson and M.B. Wise, Low-Energy Supersymmetry, Nucl. Phys. B 207 (1982) 96 [SPIRES].

    Article  ADS  Google Scholar 

  29. S. Dimopoulos and S. Raby, Geometric Hierarchy, Nucl. Phys. B 219 (1983) 479 [SPIRES].

    Article  ADS  Google Scholar 

  30. M. Dine, A.E. Nelson and Y. Shirman, Low-energy dynamical supersymmetry breaking simplified, Phys. Rev. D 51 (1995) 1362 [hep-ph/9408384] [SPIRES].

    ADS  Google Scholar 

  31. M. Dine, A.E. Nelson, Y. Nir and Y. Shirman, New tools for low-energy dynamical supersymmetry breaking, Phys. Rev. D 53 (1996) 2658 [hep-ph/9507378] [SPIRES].

    ADS  Google Scholar 

  32. A.E. Nelson and M.J. Strassler, Exact results for supersymmetric renormalization and the supersymmetric flavor problem, JHEP 07 (2002) 021 [hep-ph/0104051] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  33. T. Kobayashi and H. Terao, Sfermion masses in Nelson-Strassler type of models: SUSY standard models coupled with SCFTs, Phys. Rev. D 64 (2001) 075003 [hep-ph/0103028] [SPIRES].

    ADS  Google Scholar 

  34. R. Kitano and Y. Nomura, Supersymmetry with small mu: Connections between naturalness, dark matter and (possibly) flavor, hep-ph/0606134 [SPIRES].

  35. Y. Nomura, M. Papucci and D. Stolarski, Flavorful Supersymmetry, Phys. Rev. D 77 (2008) 075006 [arXiv:0712.2074] [SPIRES].

    ADS  Google Scholar 

  36. Y. Nomura and D. Stolarski, Naturally Flavorful Supersymmetry at the LHC, Phys. Rev. D 78 (2008) 095011 [arXiv:0808.1380] [SPIRES].

    ADS  Google Scholar 

  37. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  39. G. Mack, All Unitary Ray Representations of the Conformal Group SU(2, 2) with Positive Energy, Commun. Math. Phys. 55 (1977) 1 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  40. M. Flato and C. Fronsdal, Representations of conformal supersymmetry, Lett. Math. Phys. 8 (1984) 159 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  41. V.K. Dobrev and V.B. Petkova, All Positive Energy Unitary Irreducible Representations of Extended Conformal Supersymmetry, Phys. Lett. B 162 (1985) 127 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  42. E. Barnes, K.A. Intriligator, B. Wecht and J. Wright, Evidence for the strongest version of the 4D a-theorem, via a-maximization along RG flows, Nucl. Phys. B 702 (2004) 131 [hep-th/0408156] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  43. D. Anselmi, J. Erlich, D.Z. Freedman and A.A. Johansen, Positivity constraints on anomalies in supersymmetric gauge theories, Phys. Rev. D 57 (1998) 7570 [hep-th/9711035] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  44. D. Kutasov, A. Parnachev and D.A. Sahakyan, Central charges and U(1)R symmetries in N = 1 super Yang-Mills, JHEP 11 (2003) 013 [hep-th/0308071] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. K.A. Intriligator and B. Wecht, RG fixed points and flows in SQCD with adjoints, Nucl. Phys. B 677 (2004) 223 [hep-th/0309201] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  46. D. Kutasov, New results on the ‘a-theorem’ in four dimensional supersymmetric field theory, hep-th/0312098 [SPIRES].

  47. C. Csáki, P. Meade and J. Terning, A mixed phase of SUSY gauge theories from a-maximization, JHEP 04 (2004) 040 [hep-th/0403062] [SPIRES].

    Article  ADS  Google Scholar 

  48. E. Barnes, K.A. Intriligator, B. Wecht and J. Wright, N = 1 RG flows, product groups and a-maximization, Nucl. Phys. B 716 (2005) 33 [hep-th/0502049] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  49. K.A. Intriligator, IR free or interacting? A proposed diagnostic, Nucl. Phys. B 730 (2005) 239 [hep-th/0509085] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  50. T. Kawano, Y. Ookouchi, Y. Tachikawa and F. Yagi, Pouliot type duality via a-maximization, Nucl. Phys. B 735 (2006) 1 [hep-th/0509230] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  51. T. Kawano and F. Yagi, Supersymmetric N = 1 Spin(10) Gauge Theory with Two Spinors via a-Maximization, Nucl. Phys. B 786 (2007) 135 [arXiv:0705.4022] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  52. A.D. Shapere and Y. Tachikawa, A counterexample to the “a-theorem’, JHEP 12 (2008) 020 [arXiv:0809.3238] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  53. D. Poland, The Phase Structure of Supersymmetric Sp(2Nc) Gauge Theories with an Adjoint, JHEP 11 (2009) 049 [arXiv:0908.2131] [SPIRES].

    Article  ADS  Google Scholar 

  54. M.A. Shifman and A.I. Vainshtein, Solution of the Anomaly Puzzle in SUSY Gauge Theories and the Wilson Operator Expansion, Nucl. Phys. B 277 (1986) 456 [SPIRES].

    Article  ADS  Google Scholar 

  55. V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Exact Gell-Mann-Low Function of Supersymmetric Yang-Mills Theories from Instanton Calculus, Nucl. Phys. B 229 (1983) 381 [SPIRES].

    Article  ADS  Google Scholar 

  56. V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Supersymmetric instanton calculus: Gauge theories with matter, Nucl. Phys. B 260 (1985) 157 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  57. M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Exact Gell-Mann-Low function in supersymmetric electrodynamics, Phys. Lett. B 166 (1986) 334 [SPIRES].

    ADS  Google Scholar 

  58. L.J. Hall and Y. Nomura, A complete theory of grand unification in five dimensions, Phys. Rev. D 66 (2002) 075004 [hep-ph/0205067] [SPIRES].

    ADS  Google Scholar 

  59. D. Kutasov, A. Schwimmer and N. Seiberg, Chiral Rings, Singularity Theory and Electric-Magnetic Duality, Nucl. Phys. B 459 (1996) 455 [hep-th/9510222] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  60. D. Kutasov, A Comment on duality in N = 1 supersymmetric nonAbelian gauge theories, Phys. Lett. B 351 (1995) 230 [hep-th/9503086] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  61. K.A. Intriligator, New RG fixed points and duality in supersymmetric Sp(Nc) and SO(Nc) gauge theories, Nucl. Phys. B 448 (1995) 187 [hep-th/9505051] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  62. K.A. Intriligator and P. Pouliot, Exact superpotentials, quantum vacua and duality in supersymmetric SP(Nc) gauge theories, Phys. Lett. B 353 (1995) 471 [hep-th/9505006] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  63. R. Kitano and G.D. Kribs, Tripletless unification in the conformal window, JHEP 03 (2005) 033 [hep-ph/0501047] [SPIRES].

    Article  ADS  Google Scholar 

  64. Y. Nomura, D. Poland and B. Tweedie, Holographic Grand Unification, JHEP 12 (2006) 002 [hep-ph/0605014] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  65. R. Kitano, Dynamical GUT breaking and mu-term driven supersymmetry breaking, Phys. Rev. D 74 (2006) 115002 [hep-ph/0606129] [SPIRES].

    MathSciNet  ADS  Google Scholar 

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

    Article  MATH  MathSciNet  ADS  Google Scholar 

  67. S. Ferrara and B. Zumino, Transformation Properties Of The Supercurrent, Nucl. Phys. B 87 (1975) 207 [SPIRES].

    Article  ADS  Google Scholar 

  68. D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories, Nucl. Phys. B 526 (1998) 543 [hep-th/9708042] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  69. K.A. Intriligator, N. Seiberg and D. Shih, Dynamical SUSY breaking in meta-stable vacua, JHEP 04 (2006) 021 [hep-th/0602239] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  70. K.I. Izawa, F. Takahashi, T.T. Yanagida and K. Yonekura, Conformal Supersymmetry Breaking in Vector-like Gauge Theories, Phys. Rev. D 80 (2009) 085017 [arXiv:0905.1764] [SPIRES].

    ADS  Google Scholar 

  71. T. Banks and A. Zaks, On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions, Nucl. Phys. B 196 (1982) 189 [SPIRES].

    Article  ADS  Google Scholar 

  72. I.I. Kogan, M.A. Shifman and A.I. Vainshtein, Matching conditions and duality in N = 1 SUSY gauge theories in the conformal window, Phys. Rev. D 53 (1996) 4526 [Erratum ibid. D 59 (1999) 109903] [hep-th/9507170] [SPIRES].

    ADS  Google Scholar 

  73. M.A.A. van Leeuwen, A.M. Cohen and B. Lisser, LiE, A Package for Lie Group Computations, Computer Algebra Nederland, Amsterdam The Netherlands (1992), ISBN 90-74116-02-7.

    Google Scholar 

  74. N. Craig, Simple Models of Superconformal Flavor, arXiv:1004.4218.

Download references

Author information

Authors and Affiliations

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

    David Poland & David Simmons-Duffin

Authors
  1. David Poland
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Simmons-Duffin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Poland.

Additional information

ArXiv ePrint: 0910.4585

Rights and permissions

Reprints and permissions

About this article

Cite this article

Poland, D., Simmons-Duffin, D. Superconformal flavor simplified. J. High Energ. Phys. 2010, 79 (2010). https://doi.org/10.1007/JHEP05(2010)079

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2010)079

Keywords

Search

Navigation