The 4d/2d correspondence in twistor space and holomorphic Wilson lines

We give an explicit realization of the 4d local operator / 2d conformal block correspondence Costello and Paquette in case gauge theories. This is accomplished by lifting operators to non-local twistor space using a holomorphic generalization Wilson line. procedure automatically constructs blocks corresponding operator. interpret this as effectively integrating out degrees freedom living on defect. present some chiral CFT representations defect algebra whose correlators reproduce obtained procedure.