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Tinkertoys for the twisted D-series

  • Oscar Chacaltana
  • Jacques Distler
  • Anderson Trimm
Open Access
Regular Article - Theoretical Physics

Abstract

We study 4D \( \mathcal{N} \) = 2 superconformal field theories that arise from the compactification of 6D \( \mathcal{N} \) = (2, 0) theories of type D N on a Riemann surface, in the presence of punctures twisted by a ℤ2 outer automorphism. Unlike the untwisted case, the family of SCFTs is in general parametrized, not by ℳg,n, but by a branched cover thereof. The classification of these SCFTs is carried out explicitly in the case of the D4 theory, in terms of three-punctured spheres and cylinders, and we provide tables of properties of twisted punctures for the D5 and D6 theories. We find realizations of Spin(8) and Spin(7) gauge theories with matter in all combinations of vector and spinor representations with vanishing β-function, as well as Sp(3) gauge theories with matter in the 3-index traceless antisymmetric representation.

Keywords

Supersymmetry and Duality Extended Supersymmetry 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]
    D. Gaiotto, \( \mathcal{N} \) = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [INSPIRE].
  3. [3]
    O. Chacaltana and J. Distler, Tinkertoys for Gaiotto duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    O. Chacaltana and J. Distler, Tinkertoys for the D N series, JHEP 02 (2013) 110 [arXiv:1106.5410] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  5. [5]
    D. Nanopoulos and D. Xie, Hitchin equation, singularity and N = 2 superconformal field theories, JHEP 03 (2010) 043 [arXiv:0911.1990] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    D. Nanopoulos and D. Xie, N = 2 generalized superconformal quiver gauge theory, JHEP 09 (2012) 127 [arXiv:1006.3486] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    D. Gaiotto, G.W. Moore and Y. Tachikawa, On 6d N = (2, 0) theory compactified on a Riemann surface with finite area, Prog. Theor. Exp. Phys. 2013 (2013) 013B03 [arXiv:1110.2657] [INSPIRE].CrossRefGoogle Scholar
  8. [8]
    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].ADSCrossRefMATHGoogle Scholar
  9. [9]
    Y. Tachikawa, Six-dimensional D(N) theory and four-dimensional SO-USp quivers, JHEP 07 (2009) 067 [arXiv:0905.4074] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    Y. Tachikawa, N = 2 S-duality via outer-automorphism twists, J. Phys. A 44 (2011) 182001 [arXiv:1009.0339] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  11. [11]
    J.A. Minahan and D. Nemeschansky, An N = 2 superconformal fixed point with E 6 global symmetry, Nucl. Phys. B 482 (1996) 142 [hep-th/9608047] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  12. [12]
    J.A. Minahan and D. Nemeschansky, Superconformal fixed points with E N global symmetry, Nucl. Phys. B 489 (1997) 24 [hep-th/9610076] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  13. [13]
    P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    O. Chacaltana, J. Distler and Y. Tachikawa, Gaiotto Duality for the Twisted A 2N −1 Series, arXiv:1212.3952 [INSPIRE].
  15. [15]
    F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3D Sicilian theories, JHEP 09 (2010) 063 [arXiv:1007.0992] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    D. Gaiotto and E. Witten, S-duality of boundary conditions in N = 4 super Yang-Mills theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    D.H. Collingwood and W.M. McGovern, Nilpotent Orbits in Semisimple Lie Algebras. Van Nostrand, (1993).Google Scholar
  18. [18]
    S. Gukov and E. Witten, Rigid surface operators, Adv. Theor. Math. Phys. 14 (2010) 87 [arXiv:0804.1561] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    A. Gadde, E. Pomoni, L. Rastelli and S.S. Razamat, S-duality and 2d topological QFT, JHEP 03 (2010) 032 [arXiv:0910.2225] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    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].ADSCrossRefGoogle Scholar
  22. [22]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    M. Lemos, W. Peelaers and L. Rastelli, The superconformal index of class S theories of type D, JHEP 05 (2014) 120 [arXiv:1212.1271] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    D. Gaiotto and S.S. Razamat, Exceptional indices, JHEP 05 (2012) 145 [arXiv:1203.5517] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    N.J. Evans, C.V. Johnson and A.D. Shapere, Orientifolds, branes and duality of 4 − D gauge theories, Nucl. Phys. B 505 (1997) 251 [hep-th/9703210] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    K. Landsteiner, E. Lopez and D.A. Lowe, N = 2 supersymmetric gauge theories, branes and orientifolds, Nucl. Phys. B 507 (1997) 197 [hep-th/9705199] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    A. Brandhuber, J. Sonnenschein, S. Theisen and S. Yankielowicz, M theory and Seiberg-Witten curves: Orthogonal and symplectic groups, Nucl. Phys. B 504 (1997) 175 [hep-th/9705232] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    K. Hori, Consistency condition for five-brane in M-theory on R 5/Z(2) orbifold, Nucl. Phys. B 539 (1999) 35 [hep-th/9805141] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  29. [29]
    E.G. Gimon, On the M-theory interpretation of orientifold planes, hep-th/9806226 [INSPIRE].
  30. [30]
    Y. Tachikawa and S. Terashima, Seiberg-Witten geometries revisited, JHEP 09 (2011) 010 [arXiv:1108.2315] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Oscar Chacaltana
    • 1
  • Jacques Distler
    • 2
  • Anderson Trimm
    • 2
  1. 1.ICTP South American Institute for Fundamental Research, Instituto de Física TeóricaUniversidade Estadual PaulistaSão PauloBrazil
  2. 2.Theory Group and Texas Cosmology Center, Department of PhysicsUniversity of Texas at AustinAustinUnited States

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