Abstract
We explore extensions of the double copy to massive theories and find a new cubic theory with a local double copy. We consider the nonlinear sigma model and the special galileon theory, massless versions of which are known to be related through the double copy. We show that by performing a Kaluza-Klein reduction of these theories from five dimensions down to four, a double copy relation exists between the resulting massive four-dimensional scalar field theories. This requires the vanishing contribution of new galileon terms arising in high dimensions. We further explore if other interactions that do not arise from a dimensional reduction of the nonlinear sigma model could be double copied and find a new cubic interaction which satisfies the BCJ relations up to 5-point amplitudes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Kawai, D.C. Lewellen and S.H.H. Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
Z. Bern, J.J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, The duality between color and kinematics and its applications, arXiv:1909.01358 [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
J.J.M. Carrasco, L. Rodina, Z. Yin and S. Zekioglu, Simple encoding of higher derivative gauge and gravity counterterms, Phys. Rev. Lett. 125 (2020) 251602 [arXiv:1910.12850] [INSPIRE].
I. Low and Z. Yin, New flavor-kinematics dualities and extensions of nonlinear sigma models, Phys. Lett. B 807 (2020) 135544 [arXiv:1911.08490] [INSPIRE].
I. Low, L. Rodina and Z. Yin, Double copy in higher derivative operators of Nambu-Goldstone bosons, Phys. Rev. D 103 (2021) 025004 [arXiv:2009.00008] [INSPIRE].
J.J.M. Carrasco, L. Rodina and S. Zekioglu, Composing effective prediction at five points, JHEP 06 (2021) 169 [arXiv:2104.08370] [INSPIRE].
H.-H. Chi, H. Elvang, A. Herderschee, C.R.T. Jones and S. Paranjape, Generalizations of the double-copy: the KLT bootstrap, JHEP 03 (2022) 077 [arXiv:2106.12600] [INSPIRE].
S. Mizera, Inverse of the string theory KLT kernel, JHEP 06 (2017) 084 [arXiv:1610.04230] [INSPIRE].
L.A. Johnson, C.R.T. Jones and S. Paranjape, Constraints on a massive double-copy and applications to massive gravity, JHEP 02 (2021) 148 [arXiv:2004.12948] [INSPIRE].
A. Momeni, J. Rumbutis and A.J. Tolley, Kaluza-Klein from colour-kinematics duality for massive fields, JHEP 08 (2021) 081 [arXiv:2012.09711] [INSPIRE].
A. Momeni, J. Rumbutis and A.J. Tolley, Massive gravity from double copy, JHEP 12 (2020) 030 [arXiv:2004.07853] [INSPIRE].
M.C. González, A. Momeni and J. Rumbutis, Massive double copy in three spacetime dimensions, JHEP 08 (2021) 116 [arXiv:2107.00611] [INSPIRE].
M.C. González, A. Momeni and J. Rumbutis, Massive double copy in the high-energy limit, JHEP 04 (2022) 094 [arXiv:2112.08401] [INSPIRE].
N. Moynihan, Scattering amplitudes and the double copy in topologically massive theories, JHEP 12 (2020) 163 [arXiv:2006.15957] [INSPIRE].
N. Moynihan, Massive covariant colour-kinematics in 3D, arXiv:2110.02209 [INSPIRE].
D.J. Burger, W.T. Emond and N. Moynihan, Anyons and the double copy, JHEP 01 (2022) 017 [arXiv:2103.10416] [INSPIRE].
Y.-F. Hang and H.-J. He, Structure of Kaluza-Klein graviton scattering amplitudes from the gravitational equivalence theorem and double copy, Phys. Rev. D 105 (2022) 084005 [arXiv:2106.04568] [INSPIRE].
Y.-F. Hang, H.-J. He and C. Shen, Structure of Chern-Simons scattering amplitudes from topological equivalence theorem and double-copy, JHEP 01 (2022) 153 [arXiv:2110.05399] [INSPIRE].
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, Spontaneously broken Yang-Mills-Einstein supergravities as double copies, JHEP 06 (2017) 064 [arXiv:1511.01740] [INSPIRE].
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, Gauged supergravities and spontaneous supersymmetry breaking from the double copy construction, Phys. Rev. Lett. 120 (2018) 171601 [arXiv:1710.08796] [INSPIRE].
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, Non-Abelian gauged supergravities as double copies, JHEP 06 (2019) 099 [arXiv:1812.10434] [INSPIRE].
Y.F. Bautista and A. Guevara, On the double copy for spinning matter, JHEP 11 (2021) 184 [arXiv:1908.11349] [INSPIRE].
R. Kleiss and H. Kuijf, Multi-gluon cross-sections and five jet production at hadron colliders, Nucl. Phys. B 312 (1989) 616 [INSPIRE].
K. Hinterbichler and A. Joyce, Hidden symmetry of the Galileon, Phys. Rev. D 92 (2015) 023503 [arXiv:1501.07600] [INSPIRE].
M.C. González, R. Penco and M. Trodden, Shift symmetries, soft limits, and the double copy beyond leading order, Phys. Rev. D 102 (2020) 105011 [arXiv:1908.07531] [INSPIRE].
S. Garcia-Saenz, J. Kang and R. Penco, Gauged Galileons, JHEP 07 (2019) 081 [arXiv:1905.05190] [INSPIRE].
Z. Bern, A. De Freitas and H.L. Wong, On the coupling of gravitons to matter, Phys. Rev. Lett. 84 (2000) 3531 [hep-th/9912033] [INSPIRE].
Y.-J. Du, B. Feng and C.-H. Fu, BCJ relation of color scalar theory and KLT relation of gauge theory, JHEP 08 (2011) 129 [arXiv:1105.3503] [INSPIRE].
C.N. Pope and K.S. Stelle, SU(∞), SU+(∞) and area preserving algebras, Phys. Lett. B 226 (1989) 257 [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, R. Monteiro and D. O’Connell, Algebras for amplitudes, JHEP 06 (2012) 061 [arXiv:1203.0944] [INSPIRE].
C. Cheung, J. Mangan, J. Parra-Martinez and N. Shah, Non-perturbative double copy in flatland, arXiv:2204.07130 [INSPIRE].
M. Ben-Shahar and H. Johansson, Off-shell color-kinematics duality for Chern-Simons, arXiv:2112.11452 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2202.00620
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
González, M.C., Liang, Q. & Trodden, M. Double copy for massive scalar field theories. J. High Energ. Phys. 2022, 98 (2022). https://doi.org/10.1007/JHEP08(2022)098
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)098