Wilson lines in the MHV action
- Pennsylvania State Univ., University Park, PA (United States). Physics Dept.
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.
- Research Organization:
- Pennsylvania State Univ., University Park, PA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Nuclear Physics (NP); Polish National Science Centre (NCN)
- Grant/Contract Number:
- FG02-93ER40771; SC0002145; 2015/17/B/ST2/01838
- OSTI ID:
- 1425577
- Journal Information:
- Journal of High Energy Physics (Online), Vol. 2017, Issue 9; ISSN 1029-8479
- Publisher:
- Springer BerlinCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
The all-loop conjecture for integrands of reggeon amplitudes in N = 4 $$ \mathcal{N}=4 $$ SYM
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journal | June 2018 |
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