The Vertex Operator Algebra Vertex

Geometry, Symmetry and Physics
Event time: 
Monday, October 1, 2018 - 4:30pm
LOM 214
Miroslav Rapcak
Speaker affiliation: 
Perimeter Institute
Event description: 
Over the past two decades, Vertex Operator Algebras (VOA) have appeared in various contexts related to supersymmetric quantum field theories. I will discuss a class of VOAs arising from local operators at junctions of interfaces in the maximally symmetric four-dimensional gauge theory. The simplest trivalent junction is associated to a three-parameter family of VOAs (corner/vertex VOAs) generalizing well-known $W_N$-algebras. Vertex VOAs can be used to engineer more complicated VOAs associated to any web of trivalent junction by a gluing procedure. This construction provides us with an intuitive, pictorial way to construct and study VOAs. At the level of characters, the gluing procedure mimics the topological vertex construction of DT invariants for toric Calabi-Yau three-folds motivating the name “vertex VOA”. As an application of the newly constructed VOAs, I will propose a generalization of the AGT correspondence relating $W_N$-algebras and moduli spaces of instantons on $\mathbb{C}^2$ to the web algebras.