Nonperturbative tests of three-dimensional dualities

  • Anton Kapustin
  • Brian WillettEmail author
  • Itamar Yaakov


We test several conjectural dualities between strongly coupled superconformal field theories in three dimensions by computing their exact partition functions on a three sphere as a function of Fayet-Iliopoulos and mass parameters. The calculation is carried out using localization of the path integral and the matrix model previously derived for superconformal \( \mathcal{N} = 2 \) gauge theories. We verify that the partition functions of quiver theories related by mirror symmetry agree provided the mass parameters and the Fayet-Iliopoulos parameters are exchanged, as predicted. We carry out a similar calculation for the mirror of \( \mathcal{N} = 8 \) super-Yang-Mills theory and show that its partition function agrees with that of the ABJM theory at unit Chern-Simons level. This provides a nonperturbative test of the conjectural equivalence of the two theories in the conformal limit.


Matrix Models Brane Dynamics in Gauge Theories Extended Supersymmetry Duality in Gauge Field Theories 


  1. [1]
    K.A. Intriligator and N. Seiberg, Mirror symmetry in three dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [SPIRES].MathSciNetADSGoogle Scholar
  2. [2]
    A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [SPIRES].MathSciNetADSGoogle Scholar
  3. [3]
    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] [SPIRES].ADSGoogle Scholar
  4. [4]
    J. de Boer, K. Hori, H. Ooguri, Y. Oz and Z. Yin, Mirror symmetry in three-dimensional gauge theories, SL(2,Z) and D-brane moduli spaces, Nucl. Phys. B 493 (1997) 148 [hep-th/9612131] [SPIRES].ADSGoogle Scholar
  5. [5]
    A. Kapustin, B. Willett and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [SPIRES].CrossRefADSGoogle Scholar
  6. [6]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  7. [7]
    M.K. Benna, I.R. Klebanov and T. Klose, Charges of monopole operators in Chern-Simons Yang-Mills theory, JHEP 01 (2010) 110 [arXiv:0906.3008] [SPIRES].CrossRefADSGoogle Scholar
  8. [8]
    A. Kapustin and M.J. Strassler, On mirror symmetry in three dimensional abelian gauge theories, JHEP 04 (1999) 021 [hep-th/9902033] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  9. [9]
    E. Witten, SL(2,Z) action on three-dimensional conformal field theories with abelian symmetry, hep-th/0307041 [SPIRES].
  10. [10]
    V. Borokhov, A. Kapustin and X.-k. Wu, Monopole operators and mirror symmetry in three dimensions, JHEP 12 (2002) 044 [hep-th/0207074] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  11. [11]
    E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  12. [12]
    K. Jensen and A. Karch, ABJM mirrors and a duality of dualities, JHEP 09 (2009) 004 [arXiv:0906.3013] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  13. [13]
    S. Kim, The complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [arXiv:0903.4172] [SPIRES].CrossRefADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.California Institute of TechnologyPasadenaU.S.A.

Personalised recommendations