Appears in collection : Higher Structures in Holomorphic and Topological Field Theory

Conjecturally, one can associate a vertex operator algebra to any divisor inside a Calabi-Yau 3-fold. First, I will discuss a three-parameter family of algebras associated to a general toric divisor inside $\mathds{C}^3$. Secondly, I will sketch a gluing construction that associates an algebra to any toric divisor inside a Calabi-Yau 3-fold. The proposed algebras are expected to act naturally on the equivariant cohomology of the moduli space of Nerkasov's "spiked instantons" associated to such divisors, generalizing the famous AGT correspondence.