Wilson lines in the MHV action
Abstract
The MHV action is the YangMills action quantized on the lightfront, 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 offshell continuations of the MHV amplitudes. We show that the solution to the field transformation expressing one of the new fields in terms of the YangMills field is a certain type of the Wilson line. More precisely, it is a straight infinite gauge link with a slope extending to the lightcone minus and the transverse direction. One of the consequences of that fact is that certain MHV vertices reduced partially onshell are gauge invariant — a fact discovered before using conventional lightfront 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 lightfront 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 »
 Authors:

 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) (SC26); Polish National Science Centre (NCN)
 OSTI Identifier:
 1425577
 Grant/Contract Number:
 FG0293ER40771; 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 10298479
 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 YangMills action quantized on the lightfront, 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 offshell continuations of the MHV amplitudes. We show that the solution to the field transformation expressing one of the new fields in terms of the YangMills field is a certain type of the Wilson line. More precisely, it is a straight infinite gauge link with a slope extending to the lightcone minus and the transverse direction. One of the consequences of that fact is that certain MHV vertices reduced partially onshell are gauge invariant — a fact discovered before using conventional lightfront 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 lightfront 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 alllike helicity gluon wave function, while the inverse functional is a generating functional for solutions of selfdual YangMills 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}
}
Web of Science
Works referenced in this record:
Selfdual YangMills theory and oneloop maximally helicity violating multigluon amplitudes
journal, January 1997
 Cangemi, Daniel
 Nuclear Physics B, Vol. 484, Issue 12
Perturbative Gauge Theory as a String Theory in Twistor Space
journal, October 2004
 Witten, Edward
 Communications in Mathematical Physics, Vol. 252, Issue 13
Recursion relations and scattering amplitudes in the lightfront formalism
journal, October 2013
 CruzSantiago, C. A.; Staśto, A. M.
 Nuclear Physics B, Vol. 875, Issue 2
On amplitudes in the selfdual sector of YangMills theory
journal, April 1997
 Rosly, A. A.; Selivanov, K. G.
 Physics Letters B, Vol. 399, Issue 12
Wilson lines and gauge invariant offshell amplitudes
journal, July 2014
 Kotko, Piotr
 Journal of High Energy Physics, Vol. 2014, Issue 7
Numerical multiloop integrals and applications
journal, September 2016
 Freitas, A.
 Progress in Particle and Nuclear Physics, Vol. 90
Quantum chromodynamics and other field theories on the light cone
journal, August 1998
 Brodsky, S.
 Physics Reports, Vol. 301, Issue 46
Recursion relations for multigluon offshell amplitudes on the lightfront and Wilson lines
journal, June 2015
 CruzSantiago, C.; Kotko, P.; Staśto, A. M.
 Nuclear Physics B, Vol. 895
Gravitation in the light cone gauge
journal, December 1975
 Scherk, J.; Schwarz, John H.
 General Relativity and Gravitation, Vol. 6, Issue 6
Gauge invariant effective action for high energy processes in QCD
journal, October 1995
 Lipatov, L. N.
 Nuclear Physics B, Vol. 452, Issue 12
New recursion relations for tree amplitudes of gluons
journal, May 2005
 Britto, Ruth; Cachazo, Freddy; Feng, Bo
 Nuclear Physics B, Vol. 715, Issue 12
A selfdual YangMills 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
The Amplituhedron
journal, October 2014
 ArkaniHamed, Nima; Trnka, Jaroslav
 Journal of High Energy Physics, Vol. 2014, Issue 10
From twistor actions to MHV diagrams
journal, April 2007
 Boels, Rutger; Mason, Lionel; Skinner, David
 Physics Letters B, Vol. 648, Issue 1
BCFW recursion for offshell gluons
journal, July 2014
 van Hameren, A.
 Journal of High Energy Physics, Vol. 2014, Issue 7
MHV Vertices And Tree Amplitudes In Gauge Theory
journal, September 2004
 Cachazo, Freddy; Svrcek, Peter; Witten, Edward
 Journal of High Energy Physics, Vol. 2004, Issue 09
Recursive calculations for processes with n gluons
journal, September 1988
 Berends, F. A.; Giele, W. T.
 Nuclear Physics B, Vol. 306, Issue 4
The lagrangian origin of MHV rules
journal, March 2006
 Mansfield, Paul
 Journal of High Energy Physics, Vol. 2006, Issue 03
From YangMills lagrangian to MHV diagrams
journal, January 2006
 Gorsky, Alexander; Rosly, Aleksei
 Journal of High Energy Physics, Vol. 2006, Issue 01
Multiparton amplitudes in gauge theories
journal, February 1991
 Mangano, Michelangelo L.; Parke, Stephen J.
 Physics Reports, Vol. 200, Issue 6
Amplitude for $n$ Gluon Scattering
journal, June 1986
 Parke, Stephen J.; Taylor, T. R.
 Physical Review Letters, Vol. 56, Issue 23
Oneloop MHV rules and pure YangMills
journal, July 2007
 Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
 Journal of High Energy Physics, Vol. 2007, Issue 07
Structure of the MHVrules lagrangian
journal, August 2006
 Ettle, James H.; Morris, Tim R.
 Journal of High Energy Physics, Vol. 2006, Issue 08
Offshell 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
The MHV QCD Lagrangian
journal, August 2008
 Ettle, James H.; Morris, Tim R.; Xiao, Zhiguang
 Journal of High Energy Physics, Vol. 2008, Issue 08
Smatrix equivalence theorem evasion and dimensional regularisation with the canonical MHV lagrangian
journal, May 2007
 Ettle, James H.; Fu, ChihHao; Fudger, Jonathan P.
 Journal of High Energy Physics, Vol. 2007, Issue 05
Scattering amplitudes in the lightfront formalism
journal, November 2015
 CruzSantiago, C.; Kotko, P.; Staśto, A. M.
 Progress in Particle and Nuclear Physics, Vol. 85
Direct Proof of the TreeLevel Scattering Amplitude Recursion Relation in YangMills Theory
journal, May 2005
 Britto, Ruth; Cachazo, Freddy; Feng, Bo
 Physical Review Letters, Vol. 94, Issue 18
SelfDual YangMills Theory, Integrability and Multiparton Amplitudes
journal, January 1996
 Bardeen, William A.
 Progress of Theoretical Physics Supplement, Vol. 123
A direct proof of the CSW rules
journal, December 2005
 Risager, Kasper
 Journal of High Energy Physics, Vol. 2005, Issue 12
Works referencing / citing this record:
The allloop 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
The allloop 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