In this talk, I will explain how to obtain the space of local operators of a 4d N=2 gauge theory using the category of line operators in the Kapustin twist (holomorphic topological twist). This category is given a precise definition by Cautis-Williams, as the category of equivariant coherent sheaves on the space of Braverman-Finkelberg-Nakajima. We compute the derived endomorphism of the monoidal unit in this category, and show that it coincides with the vacuum module of the Poisson vertex algebra of Oh-Yagi and Butson. The Euler character of this space reproduces the Schur index. I will also explain how to obtain the space of local operators at the junction of minimal Wilson-t’Hooft line operators. Its Euler character can be compared to the index formula of Cordova-Gaiotto-Shao. This is based on arXiv: 2112.12164.
