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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:
 [1];  [2];  [3];  [4]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
  2. 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
  3. Univ. of California, Los Angeles, CA (United States). Mani L. Bhaumik Inst. for Theoretical Physics. Dept. of Physics and Astronomy
  4. 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:
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) (SC-25); 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.
Cheung, Clifford, Remmen, Grant N., Shen, Chia-Hsien, & Wen, Congkao. Pions as gluons in higher dimensions. United States. doi:10.1007/JHEP04(2018)129.
Cheung, Clifford, Remmen, Grant N., Shen, Chia-Hsien, and Wen, Congkao. Tue . "Pions as gluons in higher dimensions". United States. doi:10.1007/JHEP04(2018)129. https://www.osti.gov/servlets/purl/1493257.
@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 = {2018},
month = {4}
}

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Cited by: 17 works
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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


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

  • 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


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

  • 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


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

  • 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


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


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


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


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

    Works referencing / citing this record:

    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