Local Schur operators in 4d N=2 SCFTs form a protected class of operators giving rise to a 2d vertex operator algebra. Following the local operator picture, we introduce classes of conformal extended operators (lines, surfaces) and study these in twisted Schur cohomology. We show how these operators support a more general algebraic structure compared to the local operators, giving rise to an extension of the vertex algebra known for local Schur operators.

Local Schur operators in 4d N=2 SCFTs form a protected class of operators giving rise to a 2d vertex operator algebra. Following the local operator picture, we introduce classes of conformal extended operators (lines, surfaces) and study these in twisted Schur cohomology. We show how these operators support a vertex algebra structure, extending the VOA picture of local Schur operators.

In recent years, it has been understood how local operators do not paint the entire picture of a quantum field theory, but we need to introduce extended operators to understand finer details about these theories. Motivated by this, we investigate a subset of these extended operators in particular in the context of 4d N=2 superconformal field theories. I will start by introducing the setup that we use to describe the possible configurations of these extended operators. I will also compare and contrast the operators that appear in our framework with the more familiar (Wilson and 't Hooft) line operators. Time permitting, I will then introduce twists of these theories by a choice of an appropriate nilpotent supercharge. The restriction to (extended) operators living in the cohomology of this supercharge gives rise to interesting algebraic structures, that are analogous to, or rather an extension of, the 2d vertex operator algebras that have now become familiar familiar in the context of 4d N=2 theories.