Exploring straight infinite Wilson lines in the Self Dual and the MHV Lagrangians

TL;DR

This paper explores the role of straight infinite Wilson lines on the self-dual plane in connecting the Self Dual sector of Yang Mills theory with the MHV Lagrangian, providing new insights into field transformations.

Contribution

It offers a detailed analysis of Wilson lines on the self-dual plane and introduces a novel expression for the minus helicity field transformation in terms of Wilson line derivatives.

Findings

Wilson lines relate positive helicity fields to the MHV Lagrangian.

New expression for minus helicity field transformation using Wilson line derivatives.

Enhanced understanding of the connection between self-dual sector and MHV vertices.

Abstract

We investigate the appearance of straight infinite Wilson lines lying on the self-dual plane in the context of the Self Dual sector of the Yang Mills theory and in a connection to the Lagrangian implementing the MHV vertices (MHV Lagrangian) according to the Cachazo-Svrcek-Witten method. It was already recognized in the past by two of the authors, that such Wilson line functional provides the field transformation of positive helicity fields between the Yang-Mills theory on the light-cone and the MHV Lagrangian. Here we discuss in detail the connection to the Self Dual sector and we provide a new insight into the solution for the minus helicity field transformation, which can be expressed in terms of a functional derivative of the straight infinite Wilson line on the self-dual plane.