Skip to main content
SpringerLink
Log in

New \( \mathcal{N} \) =1 dualities

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

Abstract

We show that the \( \mathcal{N} \) =1 supersymmetric SU(N) gauge theory with 2N flavors without superpotential has not only the standard Seiberg dual description but also another dual description involving two copies of the so-called T N theory. This is a natural generalization to N > 2 of a dual description of SU(2) gauge theory with 4 flavors found by Csaki, Schmaltz, Skiba and Terning. We also study dualities of other \( \mathcal{N} \) =1 SCFTs involving copies of T N theories. Our duality is the basic operation from which a recently-found web of \( \mathcal{N} \) =1 dualities obtained by compactifying M5-branes on Riemann surfaces can be derived field-theoretically.

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. 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 

  2. D. Gaiotto, \( \mathcal{N} \) = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. C. Csáki, M. Schmaltz, W. Skiba and J. Terning, Selfdual \( \mathcal{N} \) = 1 SUSY gauge theories, Phys. Rev. D 56 (1997) 1228 [hep-th/9701191] [INSPIRE].

    ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  5. H. Georgi, Unparticle physics, Phys. Rev. Lett. 98 (2007) 221601 [hep-ph/0703260] [INSPIRE].

    Article  ADS  Google Scholar 

  6. P. Meade, N. Seiberg and D. Shih, General Gauge Mediation, Prog. Theor. Phys. Suppl. 177 (2009) 143 [arXiv:0801.3278] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  7. P.C. Argyres and N. Seiberg, S-duality in \( \mathcal{N} \) = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. P.C. Argyres and J.R. Wittig, Infinite coupling duals of \( \mathcal{N} \) = 2 gauge theories and new rank 1 superconformal field theories, JHEP 01 (2008) 074 [arXiv:0712.2028] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. P.C. Argyres and J. Wittig, Mass deformations of four-dimensional, rank 1, \( \mathcal{N} \) = 2 superconformal field theories, arXiv:1007.5026 [INSPIRE].

  10. O. Chacaltana and J. Distler, Tinkertoys for Gaiotto duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The 4d superconformal index from q-deformed 2d Yang-Mills, Phys. Rev. Lett. 106 (2011) 241602 [arXiv:1104.3850] [INSPIRE].

    Article  ADS  Google Scholar 

  12. A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, Gauge Theories and Macdonald Polynomials, Commun. Math. Phys. 319 (2013) 147 [arXiv:1110.3740] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. D. Gaiotto, L. Rastelli and S.S. Razamat, Bootstrapping the superconformal index with surface defects, arXiv:1207.3577 [INSPIRE].

  14. F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and \( \mathcal{N} \) = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. I. Bah and B. Wecht, New \( \mathcal{N} \) = 1 Superconformal Field Theories In Four Dimensions, arXiv:1111.3402 [INSPIRE].

  16. I. Bah, C. Beem, N. Bobev and B. Wecht, AdS/CFT Dual Pairs from M5-Branes on Riemann Surfaces, Phys. Rev. D 85 (2012) 121901 [arXiv:1112.5487] [INSPIRE].

    ADS  Google Scholar 

  17. I. Bah, C. Beem, N. Bobev and B. Wecht, Four-dimensional SCFTs from M5-branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. C. Beem and A. Gadde, The superconformal index of \( \mathcal{N} \) = 1 class S fixed points, arXiv:1212.1467 [INSPIRE].

  19. 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 

  20. P.C. Argyres, M.R. Plesser, N. Seiberg and E. Witten, New \( \mathcal{N} \) = 2 superconformal field theories in four-dimensions, Nucl. Phys. B 461 (1996) 71 [hep-th/9511154] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. D. Gaiotto, N. Seiberg and Y. Tachikawa, Comments on scaling limits of 4d \( \mathcal{N} \) = 2 theories, JHEP 01 (2011) 078 [arXiv:1011.4568] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. S. Giacomelli, Singular points in \( \mathcal{N} \) = 2 SQCD, JHEP 09 (2012) 040 [arXiv:1207.4037] [INSPIRE].

    Article  ADS  Google Scholar 

  23. Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. P.C. Argyres, K. Maruyoshi and Y. Tachikawa, Quantum Higgs branches of isolated \( \mathcal{N} \) = 2 superconformal field theories, JHEP 10 (2012) 054 [arXiv:1206.4700] [INSPIRE].

    Article  ADS  Google Scholar 

  25. P.C. Argyres, M.R. Plesser and N. Seiberg, The moduli space of vacua of \( \mathcal{N} \) = 2 SUSY QCD and duality in \( \mathcal{N} \) = 1 SUSY QCD, Nucl. Phys. B 471 (1996) 159 [hep-th/9603042] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. P.C. Argyres, K.A. Intriligator, R.G. Leigh and M.J. Strassler, On inherited duality in \( \mathcal{N} \) = 1 D = 4 supersymmetric gauge theories, JHEP 04 (2000) 029 [hep-th/9910250] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. F. Benini, S. Benvenuti and Y. Tachikawa, Webs of five-branes and \( \mathcal{N} \) = 2 superconformal field theories, JHEP 09 (2009) 052 [arXiv:0906.0359] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. O. Chacaltana, J. Distler and Y. Tachikawa, Nilpotent orbits and codimension-two defects of 6d N = (2, 0) theories, Int. J. Mod. Phys. A 28 (2013) 1340006 [arXiv:1203.2930] [INSPIRE].

    ADS  Google Scholar 

  29. J.J. Heckman, Y. Tachikawa, C. Vafa and B. Wecht, \( \mathcal{N} \) = 1 SCFTs from Brane Monodromy, JHEP 11 (2010) 132 [arXiv:1009.0017] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. D. Gaiotto and J. Maldacena, The Gravity duals of \( \mathcal{N} \) = 2 superconformal field theories, JHEP 10 (2012) 189 [arXiv:0904.4466] [INSPIRE].

    Article  ADS  Google Scholar 

  31. D. Gaiotto and S.S. Razamat, Exceptional indices, JHEP 05 (2012) 145 [arXiv:1203.5517] [INSPIRE].

    Article  ADS  Google Scholar 

  32. V. Spiridonov and G. Vartanov, Superconformal indices for \( \mathcal{N} \) = 1 theories with multiple duals, Nucl. Phys. B 824 (2010) 192 [arXiv:0811.1909] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. T. Dimofte and D. Gaiotto, An E7 surprise, JHEP 10 (2012) 129 [arXiv:1209.1404] [INSPIRE].

    Article  ADS  Google Scholar 

  34. Y. Tachikawa and B. Wecht, Explanation of the Central Charge Ratio 27/32 in Four-Dimensional Renormalization Group Flows between Superconformal Theories, Phys. Rev. Lett. 103 (2009) 061601 [arXiv:0906.0965] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  37. N. Mekareeya, J. Song and Y. Tachikawa, 2d TQFT structure of the superconformal indices with outer-automorphism twists, JHEP 03 (2013) 171 [arXiv:1212.0545] [INSPIRE].

    Article  ADS  Google Scholar 

  38. K. Maruyoshi, M. Taki, S. Terashima and F. Yagi, New Seiberg dualities from \( \mathcal{N} \) = 2 dualities, JHEP 09 (2009) 086 [arXiv:0907.2625] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. California Institute of Technology, Pasadena, CA, 91125, U.S.A.

    Abhijit Gadde, Kazunobu Maruyoshi & Wenbin Yan

  2. Department of Physics, Faculty of Science, University of Tokyo, Bunkyo-ku, Tokyo, 133-0022, Japan

    Yuji Tachikawa

  3. Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba, 277-8583, Japan

    Yuji Tachikawa

Authors
  1. Abhijit Gadde
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kazunobu Maruyoshi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuji Tachikawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenbin Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abhijit Gadde.

Additional information

ArXiv ePrint: 1303.0836

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gadde, A., Maruyoshi, K., Tachikawa, Y. et al. New \( \mathcal{N} \) =1 dualities. J. High Energ. Phys. 2013, 56 (2013). https://doi.org/10.1007/JHEP06(2013)056

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2013)056

Keywords

Search

Navigation