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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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