A large class of vertex operator algebras can be ingeneered from junctionsof interfaces in maximally upersymmetric 4d Yang-Mills theory. This viewpointprovides us with an intuitive way to study vertex operator algebras together with a link to many other physical and mathematical problems. I will describethe role of Gukov-Witten defects in four dimensions as vertex operator alegebramodules. I will determine the Zhu algebras of a class of (generically non-freely generated) W-algebras Y_{LMN} and use them to construct Zhu algebras of more complicated algebras. The techiques discussed in this talk play important role in various generalizations AGT correspondence and ramification of the geometric Langlands progam.

Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria www.ista.ac.at © ISTA 2022