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

TL;DR

This paper explicitly realizes the 4d/2d operator correspondence in gauge theories via twistor space, using holomorphic Wilson lines to construct 2d conformal blocks from 4d local operators.

Contribution

It provides a concrete method to lift 4d local operators to non-local twistor space operators, establishing a direct link to 2d conformal blocks in gauge theories.

Findings

Constructs 2d conformal blocks from 4d operators using twistor space.

Introduces holomorphic Wilson lines as a key tool.

Connects defect algebra correlators with conformal blocks.

Abstract

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