Advertisement

Notes on integral identities for 3d supersymmetric dualities

  • Nezhla Aghaei
  • Antonio Amariti
  • Yuta Sekiguchi
Open Access
Regular Article - Theoretical Physics
  • 30 Downloads

Abstract

Four dimensional \( \mathcal{N}=2 \) Argyres-Douglas theories have been recently conjectured to be described by \( \mathcal{N}=1 \) Lagrangian theories. Such models, once reduced to 3d, should be mirror dual to Lagrangian \( \mathcal{N}=4 \) theories. This has been numerically checked through the matching of the partition functions on the three sphere. In this article, we provide an analytic derivation for this result in the A2n−1 case via hyperbolic hypergeometric integrals. We study the D4 case as well, commenting on some open questions and possible resolutions. In the second part of the paper we discuss other integral identities leading to the matching of the partition functions in 3d dual pairs involving higher monopole superpotentials.

Keywords

Field Theories in Lower Dimensions Supersymmetry and Duality 

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 M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].
  2. [2]
    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
  3. [3]
    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].
  4. [4]
    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].
  5. [5]
    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
  6. [6]
    S. Benvenuti and S. Giacomelli, Abelianization and sequential confinement in 2 + 1 dimensions, JHEP 10 (2017) 173 [arXiv:1706.04949] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    S. Benvenuti and S. Giacomelli, Lagrangians for generalized Argyres-Douglas theories, JHEP 10 (2017) 106 [arXiv:1707.05113] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    P. Agarwal, A. Sciarappa and J. Song, \( \mathcal{N}=1 \) Lagrangians for generalized Argyres-Douglas theories, JHEP 10 (2017) 211 [arXiv:1707.04751] [INSPIRE].
  9. [9]
    K.A. Intriligator and B. Wecht, The exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
  10. [10]
    M. Evtikhiev, Studying superconformal symmetry enhancement through indices, arXiv:1708.08307 [INSPIRE].
  11. [11]
    D. Nanopoulos and D. Xie, More Three Dimensional Mirror Pairs, JHEP 05 (2011) 071 [arXiv:1011.1911] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    M. Buican and T. Nishinaka, Argyres-Douglas theories, S 1 reductions and topological symmetries, J. Phys. A 49 (2016) 045401 [arXiv:1505.06205] [INSPIRE].
  13. [13]
    M. Buican and T. Nishinaka, On the superconformal index of Argyres-Douglas theories, J. Phys. A 49 (2016) 015401 [arXiv:1505.05884] [INSPIRE].
  14. [14]
    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].ADSCrossRefGoogle Scholar
  15. [15]
    M. Buican and T. Nishinaka, On Irregular Singularity Wave Functions and Superconformal Indices, JHEP 09 (2017) 066 [arXiv:1705.07173] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    T.C. Collins, D. Xie and S.-T. Yau, K stability and stability of chiral ring, arXiv:1606.09260 [INSPIRE].
  17. [17]
    A. Kapustin, B. Willett and I. Yaakov, Nonperturbative Tests of Three-Dimensional Dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    F. Benini, S. Benvenuti and S. Pasquetti, SUSY monopole potentials in 2 + 1 dimensions, JHEP 08 (2017) 086 [arXiv:1703.08460] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    O. Aharony, IR duality in d = 3 N = 2 supersymmetric USp(2N c) and U(N c) gauge theories, Phys. Lett. B 404 (1997) 71 [hep-th/9703215] [INSPIRE].
  20. [20]
    D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    N. Hama, K. Hosomichi and S. Lee, SUSY Gauge Theories on Squashed Three-Spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    F. van de Bult, Hyperbolic Hypergeometric Functions, Ph.D. Thesis (2008), http://math.caltech.edu/~vdbult/Thesis.pdf.
  24. [24]
    D. Kutasov, New results on the ‘a theorem’ in four-dimensional supersymmetric field theory, hep-th/0312098 [INSPIRE].
  25. [25]
    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] [INSPIRE].
  26. [26]
    K. Nii, 3d duality with adjoint matter from 4d duality, JHEP 02 (2015) 024 [arXiv:1409.3230] [INSPIRE].
  27. [27]
    A. Amariti and C. Klare, A journey to 3d: exact relations for adjoint SQCD from dimensional reduction, JHEP 05 (2015) 148 [arXiv:1409.8623] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
  29. [29]
    K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
  30. [30]
    J. Park and K.-J. Park, Seiberg-like Dualities for 3d N = 2 Theories with SU(N) gauge group, JHEP 10 (2013) 198 [arXiv:1305.6280] [INSPIRE].
  31. [31]
    O. Aharony and D. Fleischer, IR Dualities in General 3d Supersymmetric SU(N ) QCD Theories, JHEP 02 (2015) 162 [arXiv:1411.5475] [INSPIRE].
  32. [32]
    A. Collinucci, S. Giacomelli and R. Valandro, T-branes, monopoles and S-duality, JHEP 10 (2017) 113 [arXiv:1703.09238] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    S.S. Razamat and G. Zafrir, E 8 orbits of IR dualities, JHEP 11 (2017) 115 [arXiv:1709.06106] [INSPIRE].
  34. [34]
    E.M. Rains, Transformations of elliptic hypergometric integrals, Annals Math. 171 (2010) 169 [math/0309252].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Albert Einstein Center for Fundamental Physics, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland
  2. 2.INFN, Sezione di MilanoMilanoItaly

Personalised recommendations