Mirror theories of 3d \( \mathcal{N} \) = 2 SQCD

Open Access
Regular Article - Theoretical Physics
  • 20 Downloads

Abstract

Using a recently proposed duality for U(N ) supersymmetric QCD (SQCD) in three dimensions with monopole superpotential, in this paper we derive the mirror dual description of \( \mathcal{N} \) = 2 SQCD with unitary gauge group, generalizing the known mirror dual description of abelian gauge theories. We match the chiral ring of the dual theories and their partition functions on the squashed sphere. We also conjecture a generalization for SQCD with orthogonal and symplectic gauge groups.

Keywords

Brane Dynamics in Gauge Theories Duality in Gauge Field Theories Supersymmetric Gauge Theory 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]
    K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  3. [3]
    A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    J. de Boer, K. Hori, H. Ooguri and Y. Oz, Mirror symmetry in three-dimensional gauge theories, quivers and D-branes, Nucl. Phys. B 493 (1997) 101 [hep-th/9611063] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    M. Porrati and A. Zaffaroni, M theory origin of mirror symmetry in three-dimensional gauge theories, Nucl. Phys. B 490 (1997) 107 [hep-th/9611201] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    J. de Boer, K. Hori, H. Ooguri, Y. Oz and Z. Yin, Mirror symmetry in three-dimensional theories, \( \mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right) \) and D-brane moduli spaces, Nucl. Phys. B 493 (1997) 148 [hep-th/9612131] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    J. de Boer, K. Hori, Y. Oz and Z. Yin, Branes and mirror symmetry in N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 502 (1997) 107 [hep-th/9702154] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    B. Assel, Hanany-Witten effect and \( \mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right) \) dualities in matrix models, JHEP 10 (2014) 117 [arXiv:1406.5194] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    S. Benvenuti and S. Pasquetti, 3d \( \mathcal{N} \) = 2 mirror symmetry, pq-webs and monopole superpotentials, JHEP 08 (2016) 136 [arXiv:1605.02675] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    O. Aharony, A. Hanany, K.A. Intriligator, N. Seiberg and M.J. Strassler, Aspects of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 499 (1997) 67 [hep-th/9703110] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    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
  12. [12]
    B. Assel, C. Bachas, J. Estes and J. Gomis, Holographic Duals of D = 3 N = 4 Superconformal Field Theories, JHEP 08 (2011) 087 [arXiv:1106.4253] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    S. Cremonesi, A. Hanany, N. Mekareeya and A. Zaffaroni, Coulomb branch Hilbert series and Hall-Littlewood polynomials, JHEP 09 (2014) 178 [arXiv:1403.0585] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    F. Benini, S. Benvenuti and S. Pasquetti, SUSY monopole potentials in 2+1 dimensions, JHEP 08 (2017) 086 [arXiv:1703.08460] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    A. Collinucci, S. Giacomelli, R. Savelli and R. Valandro, T-branes through 3d mirror symmetry, JHEP 07 (2016) 093 [arXiv:1603.00062] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    S. Benvenuti and S. Giacomelli, Abelianization and sequential confinement in 2 + 1 dimensions, JHEP 10 (2017) 173 [arXiv:1706.04949] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    N. Hama, K. Hosomichi and S. Lee, SUSY Gauge Theories on Squashed Three-Spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    A. Collinucci, S. Giacomelli and R. Valandro, T-branes, monopoles and S-duality, JHEP 10 (2017) 113 [arXiv:1703.09238] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    T. Dimofte, D. Gaiotto and S. Gukov, Gauge Theories Labelled by Three-Manifolds, Commun. Math. Phys. 325 (2014) 367 [arXiv:1108.4389] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    S. Benvenuti and S. Pasquetti, 3D-partition functions on the sphere: exact evaluation and mirror symmetry, JHEP 05 (2012) 099 [arXiv:1105.2551] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    M. Bullimore, H.-C. Kim and P. Koroteev, Defects and Quantum Seiberg-Witten Geometry, JHEP 05 (2015) 095 [arXiv:1412.6081] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    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].
  25. [25]
    A. Karch, Seiberg duality in three-dimensions, Phys. Lett. B 405 (1997) 79 [hep-th/9703172] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    S. Cremonesi, The Hilbert series of 3d \( \mathcal{N} \) = 2 Yang-Mills theories with vectorlike matter, J. Phys. A 48 (2015) 455401 [arXiv:1505.02409] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  27. [27]
    A. Kapustin, B. Willett and I. Yaakov, Nonperturbative Tests of Three-Dimensional Dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    S. Elitzur, A. Giveon and D. Kutasov, Branes and N = 1 duality in string theory, Phys. Lett. B 400 (1997) 269 [hep-th/9702014] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    S. Elitzur, A. Giveon, D. Kutasov, E. Rabinovici and A. Schwimmer, Brane dynamics and N = 1 supersymmetric gauge theory, Nucl. Phys. B 505 (1997) 202 [hep-th/9704104] [INSPIRE].
  30. [30]
    A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    A. Amariti, Integral identities for 3d dualities with SP(2N) gauge groups, arXiv:1509.02199 [INSPIRE].
  32. [32]
    M. Aganagic, K. Hori, A. Karch and D. Tong, Mirror symmetry in (2 + 1)-dimensions and (1 + 1)-dimensions, JHEP 07 (2001) 022 [hep-th/0105075] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    O. Aharony, S.S. Razamat and B. Willett, From 3d duality to 2d duality, JHEP 11 (2017) 090 [arXiv:1710.00926] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    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
  35. [35]
    B. Feng and A. Hanany, Mirror symmetry by O3 planes, JHEP 11 (2000) 033 [hep-th/0004092] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  36. [36]
    S. Cremonesi, A. Hanany, N. Mekareeya and A. Zaffaroni, T ρσ(G) theories and their Hilbert series, JHEP 01 (2015) 150 [arXiv:1410.1548] [INSPIRE].
  37. [37]
    S. Cabrera and A. Hanany, Branes and the Kraft-Procesi transition: classical case, arXiv:1711.02378 [INSPIRE].
  38. [38]
    A. Kapustin, D n quivers from branes, JHEP 12 (1998) 015 [hep-th/9806238] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    A. Hanany and A. Zaffaroni, Issues on orientifolds: On the brane construction of gauge theories with SO(2N ) global symmetry, JHEP 07 (1999) 009 [hep-th/9903242] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  40. [40]
    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

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.International Center for Theoretical PhysicsTriesteItaly
  2. 2.INFN, Sezione di TriesteTriesteItaly
  3. 3.INFN, Sezione di Milano-BicoccaMilanoItaly
  4. 4.Dipartimento di FisicaUniversità di Milano-BicoccaMilanoItaly

Personalised recommendations