Vertex algebra of extended operators in 4d N=2 superconformal field theories

TL;DR

This paper constructs extended operators in 4d N=2 SCFTs using twisted supercharges, revealing an enlarged vertex algebra structure through explicit computations in free hypermultiplet theories.

Contribution

It introduces a new class of extended operators derived from Schur operators via topological descent, expanding the vertex algebra of 4d N=2 SCFTs.

Findings

Extended operators are constructed from Schur operators via topological descent.

Correlators of these operators are meromorphic functions of intersection points.

Explicit OPE computations demonstrate the enlarged vertex algebra structure.

Abstract

We construct a class of extended operators in the cohomology of a pair of twisted Schur supercharges of 4d N=2 SCFTs. The extended operators are constructed from the local operators in this cohomology -- the Schur operators -- by a version of topological descent. They are line, surface, and domain wall world volume integrals of certain super descendants of Schur operators. Their world volumes extend in directions transverse to a spatial plane in Minkowski space-time. As operators in the cohomology of these twisted Schur supercharges, their correlators are (locally) meromorphic functions only of the positions where they intersect this plane. This implies the extended operators enlarge the vertex operator algebra of the Schur operators. We illustrate this enlarged vertex algebra by computing some extended-operator product expansions within a subalgebra of it for the free hypermultiplet SCFT.