Abstract
We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar fields coupled via arbitrary local interactions. Assuming perturbative unitarity and an Adler zero condition, we prove that any finite spectrum of massless and massive modes will necessarily unify at high energies into multiplets of a linearized symmetry. Certain generators of the symmetry algebra can be derived explicitly in terms of the spectrum and three-particle interactions. Furthermore, our assumptions imply that the coset space is symmetric.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Benincasa and F. Cachazo, Consistency conditions on the S-matrix of massless particles, arXiv:0705.4305 [INSPIRE].
H. Elvang and Y.-T. Huang, Scattering amplitudes in gauge theory and gravity, Cambridge University Press, Cambridge, U.K. (2015).
C. Cheung, TASI lectures on scattering amplitudes, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: anticipating the next discoveries in particle physics (TASI 2016), Boulder, CO, U.S.A., 6 June–1 July 2016, R. Essig and I. Low eds., World Scientific, Singapore (2018) [arXiv:1708.03872] [INSPIRE].
Y. Nambu, Quasiparticles and gauge invariance in the theory of superconductivity, Phys. Rev. 117 (1960) 648 [INSPIRE].
J. Goldstone, Field theories with superconductor solutions, Nuovo Cim. 19 (1961) 154 [INSPIRE].
J. Goldstone, A. Salam and S. Weinberg, Broken symmetries, Phys. Rev. 127 (1962) 965 [INSPIRE].
S. R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1, Phys. Rev. 177 (1969) 2239 [INSPIRE].
C. G. Callan, Jr., S. R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2, Phys. Rev. 177 (1969) 2247 [INSPIRE].
S. L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial vector current, Phys. Rev. 137 (1965) B1022 [INSPIRE].
S. L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial-vector current. II, Phys. Rev. 139 (1965) B1638 [INSPIRE].
I. Low, Adler’s zero and effective Lagrangians for nonlinearly realized symmetry, Phys. Rev. D 91 (2015) 105017 [arXiv:1412.2145] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny and J. Trnka, Effective field theories from soft limits of scattering amplitudes, Phys. Rev. Lett. 114 (2015) 221602 [arXiv:1412.4095] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, On-shell recursion relations for effective field theories, Phys. Rev. Lett. 116 (2016) 041601 [arXiv:1509.03309] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, A periodic table of effective field theories, JHEP 02 (2017) 020 [arXiv:1611.03137] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen, J. Trnka and C. Wen, Vector effective field theories from soft limits, Phys. Rev. Lett. 120 (2018) 261602 [arXiv:1801.01496] [INSPIRE].
H. Elvang, M. Hadjiantonis, C. R. T. Jones and S. Paranjape, Soft bootstrap and supersymmetry, JHEP 01 (2019) 195 [arXiv:1806.06079] [INSPIRE].
J. J. M. Carrasco and L. Rodina, UV considerations on scattering amplitudes in a web of theories, Phys. Rev. D 100 (2019) 125007 [arXiv:1908.08033] [INSPIRE].
J. M. Cornwall, D. N. Levin and G. Tiktopoulos, Derivation of gauge invariance from high-energy unitarity bounds on the S matrix, Phys. Rev. D 10 (1974) 1145 [Erratum ibid. 11 (1975) 972] [INSPIRE].
L. Susskind and G. Frye, Algebraic aspects of pionic duality diagrams, Phys. Rev. D 1 (1970) 1682 [INSPIRE].
C. Cheung and J. Mangan, Scattering amplitudes and the Navier-Stokes equation, arXiv:2010.15970 [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
K. Kampf, J. Novotny, M. Shifman and J. Trnka, New soft theorems for Goldstone boson amplitudes, Phys. Rev. Lett. 124 (2020) 111601 [arXiv:1910.04766] [INSPIRE].
J. Holland and B. Ion, Notes on symmetric spaces, arXiv:1211.4159 [INSPIRE].
B. W. Lee, C. Quigg and H. B. Thacker, The strength of weak interactions at very high-energies and the Higgs boson mass, Phys. Rev. Lett. 38 (1977) 883 [INSPIRE].
B. Bachu and A. Yelleshpur, On-shell electroweak sector and the Higgs mechanism, JHEP 08 (2020) 039 [arXiv:1912.04334] [INSPIRE].
G. Durieux, T. Kitahara, Y. Shadmi and Y. Weiss, The electroweak effective field theory from on-shell amplitudes, JHEP 01 (2020) 119 [arXiv:1909.10551] [INSPIRE].
J. Bonifacio and K. Hinterbichler, Unitarization from geometry, JHEP 12 (2019) 165 [arXiv:1910.04767] [INSPIRE].
J. Bonifacio and K. Hinterbichler, Bootstrap bounds on closed Einstein manifolds, JHEP 10 (2020) 069 [arXiv:2007.10337] [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: 2012.13076
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
Cheung, C., Moss, Z. Symmetry and unification from soft theorems and unitarity. J. High Energ. Phys. 2021, 161 (2021). https://doi.org/10.1007/JHEP05(2021)161
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2021)161