Wilson lines in the MHV action

• Main Authors: Kotko, P, Stasto, A. M
• Format: Journal Article
• Language: English
• Published: 31-05-2017
• Subjects: Physics - High Energy Physics - Phenomenology; Physics - High Energy Physics - Theory
• DOI: 10.48550/arxiv.1706.00052

The MHV action is the Yang-Mills action quantized on the light-front, where
the two explicit physical gluonic degrees of freedom have been canonically
transformed to a new set of fields. This transformation leads to the action
with vertices being off-shell continuations of the MHV amplitudes. We show that
the solution to the field transformation expressing one of the new fields in
terms of the Yang-Mills field is a certain type of the Wilson line. More
precisely, it is a straight infinite gauge link with a slope extending to the
light-cone minus and the transverse direction. One of the consequences of that
fact is that certain MHV vertices reduced partially on-shell are gauge
invariant -- a fact discovered before using conventional light-front
perturbation theory. We also analyze the diagrammatic content of the field
transformations leading to the MHV action. We found that the diagrams for the
solution to the transformation (given by the Wilson line) and its inverse
differ only by light-front energy denominators. Further, we investigate the
coordinate space version of the inverse solution to the one given by the Wilson
line. We find an explicit expression given by a power series in fields. We also
give a geometric interpretation to it by means of a specially defined vector
field. Finally, we discuss the fact that the Wilson line solution to the
transformation is directly related to the all-like helicity gluon wave
function, while the inverse functional is a generating functional for solutions
of self-dual Yang-Mills equations.