Abstract
We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken \( \mathcal{N}=1 \) supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.V. Volkov and V.P. Akulov, Is the neutrino a Goldstone particle?, Phys. Lett. 46B (1973) 109 [INSPIRE].
R. Kallosh, Nonlinear (super)symmetries and amplitudes, JHEP 03 (2017) 038 [arXiv:1609.09123] [INSPIRE].
B.S. DeWitt, Quantum theory of gravity. II. The manifestly covariant theory, Phys. Rev. 162 (1967) 1195 [INSPIRE].
R. Kallosh, The renormalization in non-Abelian gauge theories, Nucl. Phys. B 78 (1974) 293 [INSPIRE].
M.T. Grisaru, P. van Nieuwenhuizen and C.C. Wu, Background-field method versus normal field theory in explicit examples: one-loop divergences in S matrix and Green’s functions for Yang-Mills and gravitational fields, Phys. Rev. D 12 (1975) 3203 [INSPIRE].
J. Honerkamp, Chiral multi-loops, Nucl. Phys. B 36 (1972) 130 [INSPIRE].
I. Low, Adler’s zero and effective Lagrangians for nonlinearly realized symmetry, Phys. Rev. D 91 (2015) 105017 [arXiv:1412.2145] [INSPIRE].
I. Low, Double soft theorems and shift symmetry in nonlinear sigma models, Phys. Rev. D 93 (2016) 045032 [arXiv:1512.01232] [INSPIRE].
E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
E. Bergshoeff, F. Coomans, R. Kallosh, C.S. Shahbazi and A. Van Proeyen, Dirac-Born-Infeld-Volkov-Akulov and deformation of supersymmetry, JHEP 08 (2013) 100 [arXiv:1303.5662] [INSPIRE].
V.P. Akulov and D.V. Volkov, Goldstone fields with spin 1/2, Theor. Math. Phys. 18 (1974) 28 [INSPIRE].
B. de Wit and D.Z. Freedman, Phenomenology of Goldstone neutrinos, Phys. Rev. Lett. 35 (1975) 827 [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
R. Kallosh and T. Kugo, The footprint of E 7(7) amplitudes of \( \mathcal{N}=8 \) supergravity, JHEP 01 (2009) 072 [arXiv:0811.3414] [INSPIRE].
J. Broedel and L.J. Dixon, \( {\mathrm{\mathcal{R}}}^4 \) counterterm and E 7(7) symmetry in maximal supergravity, JHEP 05 (2010) 003 [arXiv:0911.5704] [INSPIRE].
W.-M. Chen, Y.-t. Huang and C. Wen, New fermionic soft theorems for supergravity amplitudes, Phys. Rev. Lett. 115 (2015) 021603 [arXiv:1412.1809] [INSPIRE].
H. Lüo and C. Wen, Recursion relations from soft theorems, JHEP 03 (2016) 088 [arXiv:1512.06801] [INSPIRE].
S. He, Z. Liu and J.-B. Wu, Scattering equations, twistor-string formulas and double-soft limits in four dimensions, JHEP 07 (2016) 060 [arXiv:1604.02834] [INSPIRE].
F. Cachazo, P. Cha and S. Mizera, Extensions of theories from soft limits, JHEP 06 (2016) 170 [arXiv:1604.03893] [INSPIRE].
T.E. Clark and S.T. Love, The supercurrent and spontaneously broken supersymmetry, Phys. Rev. D 39 (1989) 2391 [INSPIRE].
S.M. Kuzenko and S.A. McCarthy, On the component structure of \( \mathcal{N}=1 \) supersymmetric nonlinear electrodynamics, JHEP 05 (2005) 012 [hep-th/0501172] [INSPIRE].
Z. Komargodski and N. Seiberg, From linear SUSY to constrained superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].
S.M. Kuzenko and S.J. Tyler, Relating the Komargodski-Seiberg and Akulov-Volkov actions: exact nonlinear field redefinition, Phys. Lett. B 698 (2011) 319 [arXiv:1009.3298] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1609.09127
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Kallosh, R., Karlsson, A. & Murli, D. Origin of soft limits from nonlinear supersymmetry in Volkov-Akulov theory. J. High Energ. Phys. 2017, 81 (2017). https://doi.org/10.1007/JHEP03(2017)081
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2017)081