Networks of intertwiners, 3d theories and superalgebras


Zenkevich, Y. (2019). Networks of intertwiners, 3d theories and superalgebras. Perimeter Institute. https://pirsa.org/19020056


Zenkevich, Yegor. Networks of intertwiners, 3d theories and superalgebras. Perimeter Institute, Feb. 25, 2019, https://pirsa.org/19020056


          @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}}

Yegor Zenkevich University of California, Berkeley


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.