Networks of intertwiners, 3d theories and superalgebras

          @misc{ pirsa_PIRSA:19020056,
            doi = {10.48660/19020056},
            url = {https://pirsa.org/19020056},
            author = {Zenkevich, Yegor},
            keywords = {Mathematical physics},
            language = {en},
            title = {Networks of intertwiners, 3d theories and superalgebras},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {feb},
            note = {PIRSA:19020056 see, \url{https://pirsa.org}}
          }
          

Abstract

Refined topological vertex formalism allows one to conveniently compute partition functions of topological strings on toric CY backgrounds. These partition functions reproduce instanton partition functions of 5d N=1 gauge theories, obtained from the CY by the geometric engineering procedure. In the algebraic language the vertices can be described as intertwiners of Fock representations of a quantum toroidal algebra. I will present a «Higgsed» version of refined topological vertex formalism which computes vortex partition functions of certain N=2* 3d theories, and show how it naturally arises in the algebraic approach. The new formalism gives a streamlined way to write down the screening charges of a general class of q-deformed W-algebras, including those associated with superalgebras. The obtained partition functions are automatically eigenfunctions of Ruijsenaars-Schneider Hamiltonians or their supersymmetric generalizations.