# Networks of intertwiners, 3d theories and superalgebras

### APA

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

### MLA

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

### BibTex

@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}} }

University of Edinburgh

Talk Type

**Subject**

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.