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Argyres-Douglas matter and S-duality. Part II

  • Dan Xie
  • Ke Ye
Open Access
Regular Article - Theoretical Physics
  • 47 Downloads

Abstract

We study S-duality of Argyres-Douglas theories obtained by compactification of 6d (2,0) theories of ADE type on a sphere with irregular punctures. The weakly coupled descriptions are given by the degeneration limit of auxiliary Riemann sphere with marked points, among which three punctured sphere represents isolated superconformal theories. We also discuss twisted irregular punctures and their S-duality.

Keywords

Supersymmetry and Duality Differential and Algebraic Geometry 

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]
    P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M. Del Zotto, C. Vafa and D. Xie, Geometric engineering, mirror symmetry and \( 6{\mathrm{d}}_{\left(1,0\right)}\to 4{\mathrm{d}}_{\left(\mathcal{N}=2\right)} \), JHEP 11 (2015) 123 [arXiv:1504.08348] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    D. Xie, General Argyres-Douglas theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    M. Buican, S. Giacomelli, T. Nishinaka and C. Papageorgakis, Argyres-Douglas theories and S-duality, JHEP 02 (2015) 185 [arXiv:1411.6026] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    D. Xie and S.-T. Yau, Argyres-Douglas matter and N = 2 dualities, arXiv:1701.01123 [INSPIRE].
  8. [8]
    Y. Wang and D. Xie, Classification of Argyres-Douglas theories from M5 branes, Phys. Rev. D 94 (2016) 065012 [arXiv:1509.00847] [INSPIRE].ADSMathSciNetGoogle Scholar
  9. [9]
    D. Nanopoulos and D. Xie, Hitchin equation, irregular singularity and N = 2 asymptotical free theories, arXiv:1005.1350 [INSPIRE].
  10. [10]
    G. Bonelli, K. Maruyoshi and A. Tanzini, Wild quiver gauge theories, JHEP 02 (2012) 031 [arXiv:1112.1691] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    O. Chacaltana and J. Distler, Tinkertoys for Gaiotto duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    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].ADSCrossRefzbMATHGoogle Scholar
  13. [13]
    O. Chacaltana and J. Distler, Tinkertoys for the D N series, JHEP 02 (2013) 110 [arXiv:1106.5410] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  14. [14]
    Y. Tachikawa, Six-dimensional D(N) theory and four-dimensional SO-USp quivers, JHEP 07 (2009) 067 [arXiv:0905.4074] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    E. Sommers, Lusztig’s canonical quotient and generalized duality, J. Algebra 243 (2001) 790.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    P. Achar and E. Sommers, Local systems on nilpotent orbits and weighted Dynkin diagrams, Repr. Theor. AMS 6 (2002) 190.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    P.N. Achar, An order-reversing duality map for conjugacy classes in Lusztig’s canonical quotient, Transformation Groups 8 (2003) 107.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    D.H. Collingwood and W.M. McGovern, Nilpotent orbits in semisimple Lie algebra: an introduction, CRC Press, U.S.A. (1993).zbMATHGoogle Scholar
  19. [19]
    O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the E 6 theory, JHEP 09 (2015) 007 [arXiv:1403.4604] [INSPIRE].CrossRefzbMATHGoogle Scholar
  20. [20]
    O. Chacaltana, J. Distler, A. Trimm and Y. Zhu, Tinkertoys for the E7 theory, arXiv:1704.07890 [INSPIRE].
  21. [21]
    V. Kac, Automorphisms of finite order of semisimple Lie algebras, Funct. Anal. Appl. 3 (1969) 252.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    M. Reeder, Torsion automorphisms of simple Lie algebras, Enseign. Math. 56 (2010) 3.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    M. Reeder, P. Levy, J.-K. Yu and B.H. Gross, Gradings of positive rank on simple Lie algebras, Transformation Groups 17 (2012) 1123.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    E. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Sel. Papers (1972) 175.Google Scholar
  25. [25]
    A. Elashvili, V. Kac and E. Vinberg, Cyclic elements in semisimple Lie algebras, Transformation Groups 18 (2013) 97.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    A.D. Shapere and C. Vafa, BPS structure of Argyres-Douglas superconformal theories, hep-th/9910182 [INSPIRE].
  27. [27]
    E. Witten, Gauge theory and wild ramification, arXiv:0710.0631 [INSPIRE].
  28. [28]
    G. Kempken, Induced conjugacy classes in classical Lie-algebras, in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg volume 53, Springer, Germany (1983).Google Scholar
  29. [29]
    W.A. De Graaf and A. Elashvili, Induced nilpotent orbits of the simple Lie algebras of exceptional type, Georgian Math. J. 16 (2009) 257.MathSciNetzbMATHGoogle Scholar
  30. [30]
    F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3d Sicilian theories, JHEP 09 (2010) 063 [arXiv:1007.0992] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    D. Xie and S.-T. Yau, New N = 2 dualities, arXiv:1602.03529 [INSPIRE].
  32. [32]
    D. Nanopoulos and D. Xie, More three dimensional mirror pairs, JHEP 05 (2011) 071 [arXiv:1011.1911] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    D. Xie and P. Zhao, Central charges and RG flow of strongly-coupled N = 2 theory, JHEP 03 (2013) 006 [arXiv:1301.0210] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    A.D. Shapere and Y. Tachikawa, Central charges of N = 2 superconformal field theories in four dimensions, JHEP 09 (2008) 109 [arXiv:0804.1957] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    O. Chacaltana, J. Distler and Y. Tachikawa, Gaiotto duality for the twisted A 2N −1 series, JHEP 05 (2015) 075 [arXiv:1212.3952] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  36. [36]
    O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the twisted D-series, arXiv:1309.2299 [INSPIRE].
  37. [37]
    O. Chacaltana, J. Distler and A. Trimm, A family of 4D \( \mathcal{N}=2 \) interacting SCFTs from the twisted A 2N series, arXiv:1412.8129 [INSPIRE].
  38. [38]
    O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the twisted E 6 theory, JHEP 04 (2015) 173 [arXiv:1501.00357] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  39. [39]
    O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the Z 3 -twisted D4 theory, arXiv:1601.02077 [INSPIRE].
  40. [40]
    P.C. Argyres and J.R. Wittig, Infinite coupling duals of N = 2 gauge theories and new rank 1 superconformal field theories, JHEP 01 (2008) 074 [arXiv:0712.2028] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    Y. Tachikawa, N = 2 S-duality via Outer-automorphism Twists, J. Phys. A 44 (2011) 182001 [arXiv:1009.0339] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  42. [42]
    P. Boalch, Irregular connections and Kac-Moody root systems, arXiv:0806.1050.
  43. [43]
    A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The superconformal index of the E 6 SCFT, JHEP 08 (2010) 107 [arXiv:1003.4244] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  44. [44]
    C. Cordova and S.-H. Shao, Schur indices, BPS particles and Argyres-Douglas theories, JHEP 01 (2016) 040 [arXiv:1506.00265] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    J. Song, Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT, JHEP 02 (2016) 045 [arXiv:1509.06730] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    M. Buican and T. Nishinaka, On the superconformal index of Argyres-Douglas theories, J. Phys. A 49 (2016) 015401 [arXiv:1505.05884] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  47. [47]
    M. Buican and T. Nishinaka, On irregular singularity wave functions and superconformal indices, JHEP 09 (2017) 066 [arXiv:1705.07173] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli and B.C. van Rees, Infinite Chiral Symmetry in Four Dimensions, Commun. Math. Phys. 336 (2015) 1359 [arXiv:1312.5344] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    C. Beem and L. Rastelli, Vertex operator algebras, Higgs branches and modular differential equations, arXiv:1707.07679 [INSPIRE].
  50. [50]
    S. Gukov, D. Pei, W. Yan and K. Ye, Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality, Commun. Math. Phys. 357 (2018) 1215 [arXiv:1605.06528] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    L. Fredrickson, D. Pei, W. Yan and K. Ye, Argyres-Douglas theories, chiral algebras and wild Hitchin characters, JHEP 01 (2018) 150 [arXiv:1701.08782] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  52. [52]
    L. Fredrickson and A. Neitzke, From S 1 -fixed points to \( \mathcal{W} \) -algebra representations, arXiv:1709.06142 [INSPIRE].
  53. [53]
    S. Gukov, Trisecting non-Lagrangian theories, JHEP 11 (2017) 178 [arXiv:1707.01515] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    M. Buican, Z. Laczko and T. Nishinaka, \( \mathcal{N}=2 \) S-duality revisited, JHEP 09 (2017) 087 [arXiv:1706.03797] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  55. [55]
    K. Maruyoshi and J. Song, Enhancement of supersymmetry via renormalization group flow and the superconformal index, Phys. Rev. Lett. 118 (2017) 151602 [arXiv:1606.05632] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    K. Maruyoshi and J. Song, \( \mathcal{N}=1 \) deformations and RG flows of \( \mathcal{N}=2 \) SCFTs, JHEP 02 (2017) 075 [arXiv:1607.04281] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    P. Agarwal, K. Maruyoshi and J. Song, \( \mathcal{N}=1 \) deformations and RG flows of \( \mathcal{N}=2 \) SCFTs. Part II: non-principal deformations, JHEP 12 (2016) 103 [arXiv:1610.05311] [INSPIRE].
  58. [58]
    P. Agarwal, A. Sciarappa and J. Song, \( \mathcal{N}=1 \) Lagrangians for generalized Argyres-Douglas theories, JHEP 10 (2017) 211 [arXiv:1707.04751] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  59. [59]
    S. Benvenuti and S. Giacomelli, Supersymmetric gauge theories with decoupled operators and chiral ring stability, Phys. Rev. Lett. 119 (2017) 251601 [arXiv:1706.02225] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    S. Benvenuti and S. Giacomelli, Abelianization and sequential confinement in 2 + 1 dimensions, JHEP 10 (2017) 173 [arXiv:1706.04949] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  61. [61]
    S. Benvenuti and S. Giacomelli, Lagrangians for generalized Argyres-Douglas theories, JHEP 10 (2017) 106 [arXiv:1707.05113] [INSPIRE].
  62. [62]
    M. Caorsi and S. Cecotti, Homological S-duality in 4d N = 2 QFTs, arXiv:1612.08065 [INSPIRE].
  63. [63]
    M. Caorsi and S. Cecotti, Categorical Webs and S-duality in 4d \( \mathcal{N}=2 \) QFT, arXiv:1707.08981 [INSPIRE].
  64. [64]
    D. Xie and S.-T. Yau, 4d N = 2 SCFT and singularity theory. Part I: classification, arXiv:1510.01324 [INSPIRE].
  65. [65]
    T.A. Springer, Regular elements of finite reflection groups, Inv. Math. 25 (1974) 159.ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Center of Mathematical Sciences and ApplicationsHarvard UniversityCambridgeU.S.A.
  2. 2.Jefferson Physical LaboratoryHarvard UniversityCambridgeU.S.A.
  3. 3.Walter Burke Institute for Theoretical PhysicsCalifornia Institute of TechnologyPasadenaU.S.A.
  4. 4.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.

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