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Nonperturbative tests of three-dimensional dualities

  • Anton Kapustin
  • Brian WillettEmail author
  • Itamar Yaakov
Article

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.

Keywords

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

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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

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

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