Ring objects in the equivariant derived Satake category and 3d N=4 QFT

          @misc{ pirsa_PIRSA:18030121,
            doi = {10.48660/18030121},
            url = {https://pirsa.org/18030121},
            author = {},
            keywords = {Mathematical physics},
            language = {en},
            title = {Ring objects in the equivariant derived Satake category and 3d N=4 QFT},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {mar},
            note = {PIRSA:18030121 see, \url{https://pirsa.org}}
          }
          

Abstract

The mathematical definition of Coulomb branches of 3d N=4 gauge theories gives ring objects in the equivariant derived Satake category. We have another fundamental example of a ring object, namely the regular sheaf. It corresponds to the 3d N=4 QFT T[G], studied by Gaiotto-Witten. We also have operations on ring objects, corresponding to products, restrictions, Coulomb/Higgs gauging in the `category' of 3d N=4 QFT's. Thus we conjecture that arbitrary 3d N=4 QFT with G-symmetry gives rise a ring object in the derived Satake for G.