Pions as gluons in higher dimensions

Cheung, Clifford; Remmen, Grant N.; Shen, Chia-Hsien; Wen, Congkao

doi:10.1007/JHEP04(2018)129

Title: Pions as gluons in higher dimensions

Abstract

We derive the nonlinear sigma model as a peculiar dimensional reduction of Yang-Mills theory. In this framework, pions are reformulated as higher-dimensional gluons arranged in a kinematic configuration that only probes cubic interactions. This procedure yields a purely cubic action for the nonlinear sigma model that exhibits a symmetry enforcing color-kinematics duality. Remarkably, the associated kinematic algebra originates directly from the Poincaré algebra in higher dimensions. Applying the same construction to gravity yields a new quartic action for Born-Infeld theory and, applied once more, a cubic action for the special Galileon theory. Since the nonlinear sigma model and special Galileon are subtly encoded in the cubic sectors of Yang-Mills theory and gravity, respectively, their double copy relationship is automatic.

Authors:

Cheung, Clifford ^[1]; Remmen, Grant N. ^[2]; Shen, Chia-Hsien ^[3]; Wen, Congkao ^[4]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Univ. of California, Berkeley, CA (United States). Berkeley Center for Theoretical Physics. Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group
Univ. of California, Los Angeles, CA (United States). Mani L. Bhaumik Inst. for Theoretical Physics. Dept. of Physics and Astronomy
California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; Univ. of California, Los Angeles, CA (United States). Mani L. Bhaumik Inst. for Theoretical Physics. Dept. of Physics and Astronomy

Publication Date:: Tue Apr 24 00:00:00 EDT 2018

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

OSTI Identifier:: 1493257

Alternate Identifier(s):: OSTI ID: 1600673

Grant/Contract Number:: AC02-05CH11231; SC0010255; SC0011632; PHY-1125915; DGE-1144469

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: 2018; Journal Issue: 4; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; effective field theories; sigma models; scattering amplitudes; space-time symmetries

Citation Formats


                    Cheung, Clifford, Remmen, Grant N., Shen, Chia-Hsien, and Wen, Congkao. Pions as gluons in higher dimensions.  United States: N. p., 2018. 
Web.  doi:10.1007/JHEP04(2018)129.

Copy to clipboard


                    Cheung, Clifford, Remmen, Grant N., Shen, Chia-Hsien, & Wen, Congkao. Pions as gluons in higher dimensions.  United States.  https://doi.org/10.1007/JHEP04(2018)129

Copy to clipboard


                    Cheung, Clifford, Remmen, Grant N., Shen, Chia-Hsien, and Wen, Congkao. Tue .  
"Pions as gluons in higher dimensions".  United States.  https://doi.org/10.1007/JHEP04(2018)129.  https://www.osti.gov/servlets/purl/1493257.

Copy to clipboard


                    
@article{osti_1493257,

  title        = {Pions as gluons in higher dimensions},

  author       = {Cheung, Clifford and Remmen, Grant N. and Shen, Chia-Hsien and Wen, Congkao},

  abstractNote = {We derive the nonlinear sigma model as a peculiar dimensional reduction of Yang-Mills theory. In this framework, pions are reformulated as higher-dimensional gluons arranged in a kinematic configuration that only probes cubic interactions. This procedure yields a purely cubic action for the nonlinear sigma model that exhibits a symmetry enforcing color-kinematics duality. Remarkably, the associated kinematic algebra originates directly from the Poincaré algebra in higher dimensions. Applying the same construction to gravity yields a new quartic action for Born-Infeld theory and, applied once more, a cubic action for the special Galileon theory. Since the nonlinear sigma model and special Galileon are subtly encoded in the cubic sectors of Yang-Mills theory and gravity, respectively, their double copy relationship is automatic.},

  doi          = {10.1007/JHEP04(2018)129},

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

  number       = 4,

  volume       = 2018,

  place        = {United States},

  year         = {Tue Apr 24 00:00:00 EDT 2018},

  month        = {Tue Apr 24 00:00:00 EDT 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/JHEP04(2018)129

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 42 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

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

Monteiro, Ricardo; O’Connell, Donal
Journal of High Energy Physics, Vol. 2011, Issue 7
DOI: 10.1007/JHEP07(2011)007

Explicit BCJ numerators of nonlinear simga model
journal, September 2016

Du, Yi-Jian; Fu, Chih-Hao
Journal of High Energy Physics, Vol. 2016, Issue 9
DOI: 10.1007/JHEP09(2016)174

A relation between tree amplitudes of closed and open strings
journal, May 1986

Kawai, H.; Lewellen, D. C.; Tye, S. -H. H.
Nuclear Physics B, Vol. 269, Issue 1
DOI: 10.1016/0550-3213(86)90362-7

Symmetry for Flavor-Kinematics Duality from an Action
journal, March 2017

Cheung, Clifford; Shen, Chia-Hsien
Physical Review Letters, Vol. 118, Issue 12
DOI: 10.1103/PhysRevLett.118.121601

Semi-abelian Z-theory: NLSM+ϕ 3 from the open string
journal, August 2017

Carrasco, John Joseph M.; Mafra, Carlos R.; Schlotterer, Oliver
Journal of High Energy Physics, Vol. 2017, Issue 8
DOI: 10.1007/JHEP08(2017)135

BCJ numerators from reduced Pfaffian
journal, April 2017

Du, Yi-Jian; Teng, Fei
Journal of High Energy Physics, Vol. 2017, Issue 4
DOI: 10.1007/JHEP04(2017)033

Feynman rules for massive gauge fields with dual diagram topology
journal, September 1972

Gervais, J. L.; Neveu, A.
Nuclear Physics B, Vol. 46, Issue 2
DOI: 10.1016/0550-3213(72)90071-5

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy
journal, July 2017

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik
Journal of High Energy Physics, Vol. 2017, Issue 7
DOI: 10.1007/JHEP07(2017)002

Unifying relations for scattering amplitudes
journal, February 2018

Cheung, Clifford; Shen, Chia-Hsien; Wen, Congkao
Journal of High Energy Physics, Vol. 2018, Issue 2
DOI: 10.1007/JHEP02(2018)095

Scattering of Massless Particles in Arbitrary Dimensions
journal, October 2014

Cachazo, Freddy; He, Song; Yuan, Ellis Ye
Physical Review Letters, Vol. 113, Issue 17
DOI: 10.1103/PhysRevLett.113.171601

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

Britto, Ruth; Cachazo, Freddy; Feng, Bo
Nuclear Physics B, Vol. 715, Issue 1-2
DOI: 10.1016/j.nuclphysb.2005.02.030

On-Shell Recursion Relations for Effective Field Theories
journal, January 2016

Cheung, Clifford; Kampf, Karol; Novotny, Jiri
Physical Review Letters, Vol. 116, Issue 4
DOI: 10.1103/PhysRevLett.116.041601

Effective Field Theories from Soft Limits of Scattering Amplitudes
journal, June 2015

Cheung, Clifford; Kampf, Karol; Novotny, Jiri
Physical Review Letters, Vol. 114, Issue 22
DOI: 10.1103/PhysRevLett.114.221602

Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM
journal, July 2015

Cachazo, Freddy; He, Song; Yuan, Ellis Ye
Journal of High Energy Physics, Vol. 2015, Issue 7
DOI: 10.1007/JHEP07(2015)149

Amplitude relations in non-linear sigma model
journal, January 2014

Chen, Gang; Du, Yi-Jian
Journal of High Energy Physics, Vol. 2014, Issue 1
DOI: 10.1007/JHEP01(2014)061

Perturbative Quantum Gravity as a Double Copy of Gauge Theory
journal, August 2010

Bern, Zvi; Carrasco, John Joseph M.; Johansson, Henrik
Physical Review Letters, Vol. 105, Issue 6
DOI: 10.1103/PhysRevLett.105.061602

Perturbative spacetimes from Yang-Mills theory
journal, April 2017

Luna, Andrés; Monteiro, Ricardo; Nicholson, Isobel
Journal of High Energy Physics, Vol. 2017, Issue 4
DOI: 10.1007/JHEP04(2017)069

Nonrenormalization Theorems without Supersymmetry
journal, August 2015

Cheung, Clifford; Shen, Chia-Hsien
Physical Review Letters, Vol. 115, Issue 7
DOI: 10.1103/PhysRevLett.115.071601

A periodic table of effective field theories
journal, February 2017

Cheung, Clifford; Kampf, Karol; Novotny, Jiri
Journal of High Energy Physics, Vol. 2017, Issue 2
DOI: 10.1007/JHEP02(2017)020

Scattering of massless particles: scalars, gluons and gravitons
journal, July 2014

Cachazo, Freddy; He, Song; Yuan, Ellis Ye
Journal of High Energy Physics, Vol. 2014, Issue 7
DOI: 10.1007/JHEP07(2014)033

Twofold symmetries of the pure gravity action
journal, January 2017

Cheung, Clifford; Remmen, Grant N.
Journal of High Energy Physics, Vol. 2017, Issue 1
DOI: 10.1007/JHEP01(2017)104

Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string
journal, June 2017

Carrasco, John Joseph M.; Mafra, Carlos R.; Schlotterer, Oliver
Journal of High Energy Physics, Vol. 2017, Issue 6
DOI: 10.1007/JHEP06(2017)093

Tree-level amplitudes in the nonlinear sigma model
journal, May 2013

Kampf, Karol; Novotný, Jirí; Trnka, Jaroslav
Journal of High Energy Physics, Vol. 2013, Issue 5
DOI: 10.1007/JHEP05(2013)032

The Kinematic Algebra From the Self-Dual Sector
text, January 2011

Monteiro, Ricardo; O'Connell, Donal
arXiv
DOI: 10.48550/arxiv.1105.2565

Amplitude Relations in Non-linear Sigma Model
text, January 2013

Chen, Gang; Du, Yi-Jian
arXiv
DOI: 10.48550/arxiv.1311.1133

Non-renormalization Theorems without Supersymmetry
text, January 2015

Cheung, Clifford; Shen, Chia-Hsien
arXiv
DOI: 10.48550/arxiv.1505.01844

Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
text, January 2016

Carrasco, John Joseph M.; Mafra, Carlos R.; Schlotterer, Oliver
arXiv
DOI: 10.48550/arxiv.1608.02569

New Recursion Relations for Tree Amplitudes of Gluons
text, January 2004

Britto, Ruth; Cachazo, Freddy; Feng, Bo
arXiv
DOI: 10.48550/arxiv.hep-th/0412308

Works referencing / citing this record:

Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes
journal, February 2019

Garozzo, Lucia M.; Queimada, Leonel; Schlotterer, Oliver
Journal of High Energy Physics, Vol. 2019, Issue 2
DOI: 10.1007/jhep02(2019)078

On the kinematic algebra for BCJ numerators beyond the MHV sector
journal, November 2019

Chen, Gang; Johansson, Henrik; Teng, Fei
Journal of High Energy Physics, Vol. 2019, Issue 11
DOI: 10.1007/jhep11(2019)055

Consistency of the standard model effective field theory
journal, December 2019

Remmen, Grant N.; Rodd, Nicholas L.
Journal of High Energy Physics, Vol. 2019, Issue 12
DOI: 10.1007/jhep12(2019)032

Gravitational Radiation from Color-Kinematics Duality
text, January 2018

Shen, Chia-Hsien
arXiv
DOI: 10.48550/arxiv.1806.07388

Transmuting CHY formulae
text, January 2018

Bollmann, Max; Ferro, Livia
arXiv
DOI: 10.48550/arxiv.1808.07451

Perturbiner Methods for Effective Field Theories and the Double Copy
text, January 2018

Mizera, Sebastian; Skrzypek, Barbara
arXiv
DOI: 10.48550/arxiv.1809.02096

Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
text, January 2018

Garozzo, Lucia M.; Queimada, Leonel; Schlotterer, Oliver
arXiv
DOI: 10.48550/arxiv.1809.08103

The Infrared Structure of Exceptional Scalar Theories
text, January 2018

Yin, Zhewei
arXiv
DOI: 10.48550/arxiv.1810.07186

Soft Bootstrap and Effective Field Theories
text, January 2019

Low, Ian; Yin, Zhewei
arXiv
DOI: 10.48550/arxiv.1904.12859

On the kinematic algebra for BCJ numerators beyond the MHV sector
text, January 2019

Chen, Gang; Johansson, Henrik; Teng, Fei
arXiv
DOI: 10.48550/arxiv.1906.10683

UV considerations on scattering amplitudes in a web of theories
text, January 2019

Carrasco, John Joseph M.; Rodina, Laurentiu
arXiv
DOI: 10.48550/arxiv.1908.08033

Similar Records in DOE PAGES and OSTI.GOV collections:

Covariant color-kinematics duality

Journal Article Cheung, Clifford ; Mangan, James - Journal of High Energy Physics (Online)

We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory. For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/more »« less
https://doi.org/10.1007/jhep11(2021)069

Full Text Available
Unifying relations for scattering amplitudes

Journal Article Cheung, Clifford ; Shen, Chia-Hsien ; Wen, Congkao - Journal of High Energy Physics (Online)

We derive new amplitudes relations revealing a hidden unity among a wideranging variety of theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY constructionmore »« less
Cited by 76
https://doi.org/10.1007/jhep02(2018)095

Full Text Available
Symmetry for Flavor-Kinematics Duality from an Action

Journal Article Cheung, Clifford ; Shen, Chia-Hsien - Physical Review Letters

In this paper, we propose a new representation of the nonlinear sigma model that exhibits a manifest duality between flavor and kinematics. The fields couple exclusively through cubic Feynman vertices which define the structure constants of an underlying kinematic algebra. The action is invariant under a combination of internal and spacetime symmetries whose conservation equations imply flavor-kinematics duality, ensuring that all Feynman diagrams satisfy kinematic Jacobi identities. Substituting flavor for kinematics, we derive a new cubic action for the special Galileon theory. Finally, in this picture, the vanishing soft behavior of amplitudes is a by-product of the Weinberg soft theorem.
Cited by 66
https://doi.org/10.1103/PhysRevLett.118.121601

Full Text Available
On-Shell Recursion Relations for Effective Field Theories

Journal Article Cheung, Clifford ; Kampf, Karol ; Novotny, Jiri ; ... - Physical Review Letters

We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible.
Cited by 114
https://doi.org/10.1103/PhysRevLett.116.041601
Cartan gravity, matter fields, and the gauge principle

Journal Article Westman, Hans F., E-mail: hwestman74@gmail.com ; Zlosnik, Tom G., E-mail: t.zlosnik@imperial.ac.uk - Annals of Physics (New York)

Gravity is commonly thought of as one of the four force fields in nature. However, in standard formulations its mathematical structure is rather different from the Yang–Mills fields of particle physics that govern the electromagnetic, weak, and strong interactions. This paper explores this dissonance with particular focus on how gravity couples to matter from the perspective of the Cartan-geometric formulation of gravity. There the gravitational field is represented by a pair of variables: (1) a ‘contact vector’ V{sup A} which is geometrically visualized as the contact point between the spacetime manifold and a model spacetime being ‘rolled’ on top ofmore »« less
https://doi.org/10.1016/J.AOP.2013.03.012

Similar Records

Title: Pions as gluons in higher dimensions

Abstract

Citation Formats

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

Explicit BCJ numerators of nonlinear simga model journal, September 2016

A relation between tree amplitudes of closed and open strings journal, May 1986

Symmetry for Flavor-Kinematics Duality from an Action journal, March 2017

Semi-abelian Z-theory: NLSM+ϕ 3 from the open string journal, August 2017

BCJ numerators from reduced Pfaffian journal, April 2017

Feynman rules for massive gauge fields with dual diagram topology journal, September 1972

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy journal, July 2017

Unifying relations for scattering amplitudes journal, February 2018

Scattering of Massless Particles in Arbitrary Dimensions journal, October 2014

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

On-Shell Recursion Relations for Effective Field Theories journal, January 2016

Effective Field Theories from Soft Limits of Scattering Amplitudes journal, June 2015

Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM journal, July 2015

Amplitude relations in non-linear sigma model journal, January 2014

Perturbative Quantum Gravity as a Double Copy of Gauge Theory journal, August 2010

Perturbative spacetimes from Yang-Mills theory journal, April 2017

Nonrenormalization Theorems without Supersymmetry journal, August 2015

A periodic table of effective field theories journal, February 2017

Scattering of massless particles: scalars, gluons and gravitons journal, July 2014

Twofold symmetries of the pure gravity action journal, January 2017

Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string journal, June 2017

Tree-level amplitudes in the nonlinear sigma model journal, May 2013

The Kinematic Algebra From the Self-Dual Sector text, January 2011

Amplitude Relations in Non-linear Sigma Model text, January 2013

Non-renormalization Theorems without Supersymmetry text, January 2015

Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string text, January 2016

New Recursion Relations for Tree Amplitudes of Gluons text, January 2004

Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes journal, February 2019

On the kinematic algebra for BCJ numerators beyond the MHV sector journal, November 2019

Consistency of the standard model effective field theory journal, December 2019

Gravitational Radiation from Color-Kinematics Duality text, January 2018

Transmuting CHY formulae text, January 2018

Perturbiner Methods for Effective Field Theories and the Double Copy text, January 2018

Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes text, January 2018

The Infrared Structure of Exceptional Scalar Theories text, January 2018

Soft Bootstrap and Effective Field Theories text, January 2019

On the kinematic algebra for BCJ numerators beyond the MHV sector text, January 2019

UV considerations on scattering amplitudes in a web of theories text, January 2019

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

Explicit BCJ numerators of nonlinear simga model
journal, September 2016

A relation between tree amplitudes of closed and open strings
journal, May 1986

Symmetry for Flavor-Kinematics Duality from an Action
journal, March 2017

Semi-abelian Z-theory: NLSM+ϕ 3 from the open string
journal, August 2017

BCJ numerators from reduced Pfaffian
journal, April 2017

Feynman rules for massive gauge fields with dual diagram topology
journal, September 1972

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy
journal, July 2017

Unifying relations for scattering amplitudes
journal, February 2018

Scattering of Massless Particles in Arbitrary Dimensions
journal, October 2014

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

On-Shell Recursion Relations for Effective Field Theories
journal, January 2016

Effective Field Theories from Soft Limits of Scattering Amplitudes
journal, June 2015

Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM
journal, July 2015

Amplitude relations in non-linear sigma model
journal, January 2014

Perturbative Quantum Gravity as a Double Copy of Gauge Theory
journal, August 2010

Perturbative spacetimes from Yang-Mills theory
journal, April 2017

Nonrenormalization Theorems without Supersymmetry
journal, August 2015

A periodic table of effective field theories
journal, February 2017

Scattering of massless particles: scalars, gluons and gravitons
journal, July 2014

Twofold symmetries of the pure gravity action
journal, January 2017

Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string
journal, June 2017

Tree-level amplitudes in the nonlinear sigma model
journal, May 2013

The Kinematic Algebra From the Self-Dual Sector
text, January 2011

Amplitude Relations in Non-linear Sigma Model
text, January 2013

Non-renormalization Theorems without Supersymmetry
text, January 2015

Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
text, January 2016

New Recursion Relations for Tree Amplitudes of Gluons
text, January 2004

Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes
journal, February 2019

On the kinematic algebra for BCJ numerators beyond the MHV sector
journal, November 2019

Consistency of the standard model effective field theory
journal, December 2019

Gravitational Radiation from Color-Kinematics Duality
text, January 2018

Transmuting CHY formulae
text, January 2018

Perturbiner Methods for Effective Field Theories and the Double Copy
text, January 2018

Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
text, January 2018

The Infrared Structure of Exceptional Scalar Theories
text, January 2018

Soft Bootstrap and Effective Field Theories
text, January 2019

On the kinematic algebra for BCJ numerators beyond the MHV sector
text, January 2019

UV considerations on scattering amplitudes in a web of theories
text, January 2019