A new Wilson line-based action for gluodynamics

Kakkad, Hiren; Kotko, Piotr; Stasto, Anna

doi:10.1007/jhep07(2021)187

Title: A new Wilson line-based action for gluodynamics

Abstract

We perform a canonical transformation of fields that brings the Yang-Mills action in the light-cone gauge to a new classical action, which does not involve any triple-gluon vertices. The lowest order vertex is the four-point MHV vertex. Higher point vertices include the MHV and $$\overline{\mathrm{MHV}}$$ vertices, that reduce to the corresponding amplitudes in the on-shell limit. In general, anyn-leg vertex has 2≤ m ≤ n -2 negative helicity legs. The canonical transformation of fields can be compactly expressed in terms of path-ordered exponentials of fields and their functional derivative. We apply the new action to compute several tree-level amplitudes, up to 8-point NNMHV amplitude, and find agreement with the standard methods. The absence of triple-gluon vertices results in fewer diagrams required to compute amplitudes, when compared to the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action.

Authors:

^[1];

^[2]

AGH - Univ. of Science and Technology, Krakow (Poland). Faculty of Physics
Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)

Publication Date:: 2021-07-23

Research Org.:: Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1850798

Grant/Contract Number:: SC0002145

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: 2021; Journal Issue: 7; Journal ID: ISSN 1029-8479

Publisher:: Springer Nature

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Effective Field Theories; Gauge Symmetry; Scattering Amplitudes

Citation Formats


                    Kakkad, Hiren, Kotko, Piotr, and Stasto, Anna. A new Wilson line-based action for gluodynamics.  United States: N. p., 2021. 
Web.  doi:10.1007/jhep07(2021)187.

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                    Kakkad, Hiren, Kotko, Piotr, & Stasto, Anna. A new Wilson line-based action for gluodynamics.  United States.  https://doi.org/10.1007/jhep07(2021)187

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                    Kakkad, Hiren, Kotko, Piotr, and Stasto, Anna. Fri .  
"A new Wilson line-based action for gluodynamics".  United States.  https://doi.org/10.1007/jhep07(2021)187.  https://www.osti.gov/servlets/purl/1850798.

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@article{osti_1850798,

  title        = {A new Wilson line-based action for gluodynamics},

  author       = {Kakkad, Hiren and Kotko, Piotr and Stasto, Anna},

  abstractNote = {We perform a canonical transformation of fields that brings the Yang-Mills action in the light-cone gauge to a new classical action, which does not involve any triple-gluon vertices. The lowest order vertex is the four-point MHV vertex. Higher point vertices include the MHV and $\overline{\mathrm{MHV}}$ vertices, that reduce to the corresponding amplitudes in the on-shell limit. In general, anyn-leg vertex has 2≤ m ≤ n -2 negative helicity legs. The canonical transformation of fields can be compactly expressed in terms of path-ordered exponentials of fields and their functional derivative. We apply the new action to compute several tree-level amplitudes, up to 8-point NNMHV amplitude, and find agreement with the standard methods. The absence of triple-gluon vertices results in fewer diagrams required to compute amplitudes, when compared to the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action.},

  doi          = {10.1007/jhep07(2021)187},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 7,

  volume       = 2021,

  place        = {United States},

  year         = {2021},

  month        = {7}

}

Copy to clipboard

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Title: A new Wilson line-based action for gluodynamics

Abstract

Citation Formats

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

MHV Lagrangian for N = 4 super Yang-Mills journal, April 2009

Non-supersymmetric loop amplitudes and MHV vertices journal, April 2005

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

Gauge fields as rings of glue journal, January 1980

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

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

Gravitation in the light cone gauge journal, December 1975

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

One-loop gauge theory amplitudes in super Yang–Mills from MHV vertices journal, January 2005

S@M, a mathematica implementation of the spinor-helicity formalism journal, October 2008

The Color Glass Condensate journal, November 2010

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

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

The lagrangian origin of MHV rules journal, March 2006

Integrands for QCD rational terms and $ \mathcal{N} = {4} $ SYM from massive CSW rules journal, June 2012

The kinematic algebra from the self-dual sector journal, July 2011

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

Exact kinematics in the small- x evolution of the color dipole and gluon cascade journal, April 2009

Self-dual sector of QCD amplitudes journal, December 1996

Generating MHV super-vertices in light-cone gauge journal, April 2010

Amplitudes in pure Yang-Mills and MHV Diagrams journal, February 2007

The MHV Lagrangian for a spontaneously broken gauge theory journal, September 2010

Structure of the MHV-rules lagrangian journal, August 2006

Exploring straight infinite Wilson lines in the self-dual and the MHV Lagrangians journal, November 2020

The MHV QCD Lagrangian journal, August 2008

A twistor approach to one-loop amplitudes in supersymmetric Yang–Mills theory journal, January 2005

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

The canonical transformation and massive CSW vertices for MHV-SQCD journal, December 2008

All tree-level amplitudes in massless QCD journal, January 2011

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

Light-cone recurrence relations for QCD amplitudes journal, April 1990

A direct proof of the CSW rules journal, December 2005

Deriving CSW rules for massive scalar legs and pure Yang-Mills loops journal, July 2008

Wilson lines in the MHV action journal, September 2017

A direct proof of the CSW rules journal, December 2005

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

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

Exploring straight infinite Wilson lines in the Self Dual and the MHV Lagrangians text, January 2020

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

MHV Lagrangian for N = 4 super Yang-Mills
journal, April 2009

Non-supersymmetric loop amplitudes and MHV vertices
journal, April 2005

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

Gauge fields as rings of glue
journal, January 1980

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

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

Gravitation in the light cone gauge
journal, December 1975

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

One-loop gauge theory amplitudes in super Yang–Mills from MHV vertices
journal, January 2005

S@M, a mathematica implementation of the spinor-helicity formalism
journal, October 2008

The Color Glass Condensate
journal, November 2010

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

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

The lagrangian origin of MHV rules
journal, March 2006

Integrands for QCD rational terms and $ \mathcal{N} = {4} $ SYM from massive CSW rules
journal, June 2012

The kinematic algebra from the self-dual sector
journal, July 2011

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

Exact kinematics in the small- $x$ evolution of the color dipole and gluon cascade
journal, April 2009

Self-dual sector of QCD amplitudes
journal, December 1996

Generating MHV super-vertices in light-cone gauge
journal, April 2010

Amplitudes in pure Yang-Mills and MHV Diagrams
journal, February 2007

The MHV Lagrangian for a spontaneously broken gauge theory
journal, September 2010

Structure of the MHV-rules lagrangian
journal, August 2006

Exploring straight infinite Wilson lines in the self-dual and the MHV Lagrangians
journal, November 2020

The MHV QCD Lagrangian
journal, August 2008

A twistor approach to one-loop amplitudes in supersymmetric Yang–Mills theory
journal, January 2005

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

The canonical transformation and massive CSW vertices for MHV-SQCD
journal, December 2008

All tree-level amplitudes in massless QCD
journal, January 2011

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

Light-cone recurrence relations for QCD amplitudes
journal, April 1990

A direct proof of the CSW rules
journal, December 2005

Deriving CSW rules for massive scalar legs and pure Yang-Mills loops
journal, July 2008

Wilson lines in the MHV action
journal, September 2017

A direct proof of the CSW rules
journal, December 2005

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

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

Exploring straight infinite Wilson lines in the Self Dual and the MHV Lagrangians
text, January 2020