skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Wilson lines in the MHV action

Abstract

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 interpretationmore » 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.« less

Authors:
 [1];  [1]
  1. Pennsylvania State Univ., University Park, PA (United States). Physics Dept.
Publication Date:
Research Org.:
Pennsylvania State Univ., University Park, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); Polish National Science Centre (NCN)
OSTI Identifier:
1425577
Grant/Contract Number:  
FG02-93ER40771; SC0002145; 2015/17/B/ST2/01838
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; scattering amplitudes; perturbative QCD

Citation Formats

Kotko, P., and Stasto, A. M. Wilson lines in the MHV action. United States: N. p., 2017. Web. doi:10.1007/JHEP09(2017)047.
Kotko, P., & Stasto, A. M. Wilson lines in the MHV action. United States. doi:10.1007/JHEP09(2017)047.
Kotko, P., and Stasto, A. M. Tue . "Wilson lines in the MHV action". United States. doi:10.1007/JHEP09(2017)047. https://www.osti.gov/servlets/purl/1425577.
@article{osti_1425577,
title = {Wilson lines in the MHV action},
author = {Kotko, P. and Stasto, A. M.},
abstractNote = {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.},
doi = {10.1007/JHEP09(2017)047},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2017,
place = {United States},
year = {2017},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Self-dual Yang-Mills theory and one-loop maximally helicity violating multi-gluon amplitudes
journal, January 1997


Perturbative Gauge Theory as a String Theory in Twistor Space
journal, October 2004


Recursion relations and scattering amplitudes in the light-front formalism
journal, October 2013


On amplitudes in the self-dual sector of Yang-Mills theory
journal, April 1997


Wilson lines and gauge invariant off-shell amplitudes
journal, July 2014


Numerical multi-loop integrals and applications
journal, September 2016


Quantum chromodynamics and other field theories on the light cone
journal, August 1998


Recursion relations for multi-gluon off-shell amplitudes on the light-front and Wilson lines
journal, June 2015


Gravitation in the light cone gauge
journal, December 1975

  • Scherk, J.; Schwarz, John H.
  • General Relativity and Gravitation, Vol. 6, Issue 6
  • DOI: 10.1007/BF00761962

Gauge invariant effective action for high energy processes in QCD
journal, October 1995


New recursion relations for tree amplitudes of gluons
journal, May 2005


A self-dual Yang-Mills hierarchy and its reductions to integrable systems in 1+1 and 2+1 dimensions
journal, November 1993

  • Ablowitz, Mark J.; Chakravarty, Sarbarish; Takhtajan, Leon A.
  • Communications in Mathematical Physics, Vol. 158, Issue 2
  • DOI: 10.1007/BF02108076

The Amplituhedron
journal, October 2014

  • Arkani-Hamed, Nima; Trnka, Jaroslav
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)030

From twistor actions to MHV diagrams
journal, April 2007


BCFW recursion for off-shell gluons
journal, July 2014


MHV Vertices And Tree Amplitudes In Gauge Theory
journal, September 2004


Recursive calculations for processes with n gluons
journal, September 1988


The lagrangian origin of MHV rules
journal, March 2006


From Yang-Mills lagrangian to MHV diagrams
journal, January 2006


Multi-parton amplitudes in gauge theories
journal, February 1991


Amplitude for n -Gluon Scattering
journal, June 1986


One-loop MHV rules and pure Yang-Mills
journal, July 2007


Structure of the MHV-rules lagrangian
journal, August 2006


Off-shell amplitudes as boundary integrals of analytically continued Wilson line slope
journal, August 2016

  • Kotko, P.; Serino, M.; Stasto, A. M.
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)026

The MHV QCD Lagrangian
journal, August 2008


S-matrix equivalence theorem evasion and dimensional regularisation with the canonical MHV lagrangian
journal, May 2007


Scattering amplitudes in the light-front formalism
journal, November 2015


Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory
journal, May 2005


Self-Dual Yang-Mills Theory, Integrability and Multiparton Amplitudes
journal, January 1996

  • Bardeen, William A.
  • Progress of Theoretical Physics Supplement, Vol. 123
  • DOI: 10.1143/PTPS.123.1

A direct proof of the CSW rules
journal, December 2005


    Works referencing / citing this record:

    The all-loop conjecture for integrands of reggeon amplitudes in N = 4 $$ \mathcal{N}=4 $$ SYM
    journal, June 2018

    • Bolshov, A. E.; Bork, L. V.; Onishchenko, A. I.
    • Journal of High Energy Physics, Vol. 2018, Issue 6
    • DOI: 10.1007/jhep06(2018)129

    The all-loop conjecture for integrands of reggeon amplitudes in N = 4 $$ \mathcal{N}=4 $$ SYM
    journal, June 2018

    • Bolshov, A. E.; Bork, L. V.; Onishchenko, A. I.
    • Journal of High Energy Physics, Vol. 2018, Issue 6
    • DOI: 10.1007/jhep06(2018)129