Abstract
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.
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References
K.A. Intriligator and N. Seiberg, Mirror symmetry in three dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [SPIRES].
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].
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].
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].
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].
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].
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].
A. Kapustin and M.J. Strassler, On mirror symmetry in three dimensional abelian gauge theories, JHEP 04 (1999) 021 [hep-th/9902033] [SPIRES].
E. Witten, SL(2,Z) action on three-dimensional conformal field theories with abelian symmetry, hep-th/0307041 [SPIRES].
V. Borokhov, A. Kapustin and X.-k. Wu, Monopole operators and mirror symmetry in three dimensions, JHEP 12 (2002) 044 [hep-th/0207074] [SPIRES].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [SPIRES].
K. Jensen and A. Karch, ABJM mirrors and a duality of dualities, JHEP 09 (2009) 004 [arXiv:0906.3013] [SPIRES].
S. Kim, The complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [arXiv:0903.4172] [SPIRES].
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ArXiv ePrint: 1003.5694
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Kapustin, A., Willett, B. & Yaakov, I. Nonperturbative tests of three-dimensional dualities. J. High Energ. Phys. 2010, 13 (2010). https://doi.org/10.1007/JHEP10(2010)013
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DOI: https://doi.org/10.1007/JHEP10(2010)013