3d mirror symmetry as a canonical transformation

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14 Citations (Scopus)


Abstract: We generalize the free Fermi-gas formulation of certain 3d N=3$$ \mathcal{N}=3 $$ super-symmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos couplings as well as mass terms for bifundamental matter fields. The resulting partition functions are given by simple modifications of the argument of the Airy function found previously. With these extra parameters it is easy to see that mirror-symmetry corresponds to linear canonical transformations on the phase space (or operator algebra) of the 1-dimensional fermions.

Original languageEnglish
Article number4
Number of pages13
JournalJournal of High Energy Physics
Issue number5
Publication statusPublished - 4 May 2015


  • Chern-Simons Theories
  • Duality in Gauge Field Theories
  • Matrix Models
  • Supersymmetric gauge theory


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