Abstract
The dynamics of the Goldstino mode of spontaneously broken supersymmetry is universal, being fully determined by the non-linearly realized symmetry. We investigate the small-field limit of this theory. This model non-linearly realizes an alternative supersymmetry algebra with vanishing anti-commutators between the fermionic generators, much like an internal supersymmetry. This Goldstino theory is akin to the Galilean scalar field theory that arises as the small-field limit of Dirac-Born-Infeld theory and non-linearly realizes the Galilean symmetry. Indeed, the small-field Goldstino is the partner of a complex Galilean scalar field under conventional supersymmetry. We close with the generalization to extended internal supersymmetry and a discussion of its higher-dimensional origin.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
D.V. Volkov, Phenomenological Lagrangians, Fiz. Elem. Chast. Atom. Yadra 4 (1973) 3.
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, A Periodic Table of Effective Field Theories, JHEP 02 (2017) 020 [arXiv:1611.03137] [INSPIRE].
A. Padilla, D. Stefanyszyn and T. Wilson, Probing Scalar Effective Field Theories with the Soft Limits of Scattering Amplitudes, JHEP 04 (2017) 015 [arXiv:1612.04283] [INSPIRE].
C. de Rham and A.J. Tolley, DBI and the Galileon reunited, JCAP 05 (2010) 015 [arXiv:1003.5917] [INSPIRE].
K. Hinterbichler, M. Trodden and D. Wesley, Multi-field galileons and higher co-dimension branes, Phys. Rev. D 82 (2010) 124018 [arXiv:1008.1305] [INSPIRE].
G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, Galileons as Wess-Zumino Terms, JHEP 06 (2012) 004 [arXiv:1203.3191] [INSPIRE].
G.R. Dvali, G. Gabadadze and M. Porrati, 4-D gravity on a brane in 5-D Minkowski space, Phys. Lett. B 485 (2000) 208 [hep-th/0005016] [INSPIRE].
K. Hinterbichler, Theoretical Aspects of Massive Gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].
C. Deffayet, G. Esposito-Farese and A. Vikman, Covariant Galileon, Phys. Rev. D 79 (2009) 084003 [arXiv:0901.1314] [INSPIRE].
S. Peirone, N. Frusciante, B. Hu, M. Raveri and A. Silvestri, Do current cosmological observations rule out all Covariant Galileons?, Phys. Rev. D 97 (2018) 063518 [arXiv:1711.04760] [INSPIRE].
D.V. Volkov and V.P. Akulov, Is the Neutrino a Goldstone Particle?, Phys. Lett. B 46 (1973) 109 [INSPIRE].
E.A. Ivanov and A.A. Kapustnikov, General Relationship Between Linear and Nonlinear Realizations of Supersymmetry, J. Phys. A 11 (1978) 2375 [INSPIRE].
E.A. Ivanov and A.A. Kapustnikov, The nonlinear realization structure of models with spontaneously broken supersymmetry, J. Phys. G 8 (1982) 167 [INSPIRE].
C. Deffayet, A.E. Gümrükçüoglu, S. Mukohyama and Y. Wang, A no-go theorem for generalized vector Galileons on flat spacetime, JHEP 04 (2014) 082 [arXiv:1312.6690] [INSPIRE].
R. Kallosh, Volkov-Akulov theory and D-branes, hep-th/9705118 [INSPIRE].
R. Kallosh, A. Karlsson and D. Murli, Origin of Soft Limits from Nonlinear Supersymmetry in Volkov-Akulov Theory, JHEP 03 (2017) 081 [arXiv:1609.09127] [INSPIRE].
R. Haag, J.T. Lopuszanski and M. Sohnius, All Possible Generators of Supersymmetries of the s Matrix, Nucl. Phys. B 88 (1975) 257 [INSPIRE].
S.R. Coleman and J. Mandula, All Possible Symmetries of the S Matrix, Phys. Rev. 159 (1967) 1251 [INSPIRE].
J. Bagger and A. Galperin, A new Goldstone multiplet for partially broken supersymmetry, Phys. Rev. D 55 (1997) 1091 [hep-th/9608177] [INSPIRE].
J. Bagger and A. Galperin, The tensor Goldstone multiplet for partially broken supersymmetry, Phys. Lett. B 412 (1997) 296 [hep-th/9707061] [INSPIRE].
M. Roček and A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields and three-brane actions, Phys. Rev. D 59 (1999) 106001 [hep-th/9811232] [INSPIRE].
F. Gonzalez-Rey, I.Y. Park and M. Roček, On dual 3-brane actions with partially broken N = 2 supersymmetry, Nucl. Phys. B 544 (1999) 243 [hep-th/9811130] [INSPIRE].
B. Bellazzini, Softness and amplitudes’ positivity for spinning particles, JHEP 02 (2017) 034 [arXiv:1605.06111] [INSPIRE].
D. Liu, A. Pomarol, R. Rattazzi and F. Riva, Patterns of Strong Coupling for LHC Searches, JHEP 11 (2016) 141 [arXiv:1603.03064] [INSPIRE].
B. Bellazzini, F. Riva, J. Serra and F. Sgarlata, The other effective fermion compositeness, JHEP 11 (2017) 020 [arXiv:1706.03070] [INSPIRE].
H. Abe, Y. Sakamura and Y. Yamada, N = 1 superfield description of vector-tensor couplings in six dimensions, JHEP 04 (2015) 035 [arXiv:1501.07642] [INSPIRE].
K. Hinterbichler and A. Joyce, Hidden symmetry of the Galileon, Phys. Rev. D 92 (2015) 023503 [arXiv:1501.07600] [INSPIRE].
J. Khoury, J.-L. Lehners and B. Ovrut, Supersymmetric P (X, ϕ) and the Ghost Condensate, Phys. Rev. D 83 (2011) 125031 [arXiv:1012.3748] [INSPIRE].
M. Koehn, J.-L. Lehners and B. Ovrut, Supersymmetric cubic Galileons have ghosts, Phys. Rev. D 88 (2013) 023528 [arXiv:1302.0840] [INSPIRE].
F. Farakos, C. Germani and A. Kehagias, On ghost-free supersymmetric galileons, JHEP 11 (2013) 045 [arXiv:1306.2961] [INSPIRE].
J.M. Queiruga, Supersymmetric galileons and auxiliary fields in 2+1 dimensions, Phys. Rev. D 95 (2017) 125001 [arXiv:1612.04727] [INSPIRE].
H. Motohashi, K. Noui, T. Suyama, M. Yamaguchi and D. Langlois, Healthy degenerate theories with higher derivatives, JCAP 07 (2016) 033 [arXiv:1603.09355] [INSPIRE].
R. Klein and D. Roest, Exorcising the Ostrogradsky ghost in coupled systems, JHEP 07 (2016) 130 [arXiv:1604.01719] [INSPIRE].
R. Kimura, Y. Sakakihara and M. Yamaguchi, Ghost free systems with coexisting bosons and fermions, Phys. Rev. D 96 (2017) 044015 [arXiv:1704.02717] [INSPIRE].
R. Kallosh, Nonlinear (Super)Symmetries and Amplitudes, JHEP 03 (2017) 038 [arXiv:1609.09123] [INSPIRE].
J. Hughes, J. Liu and J. Polchinski, Supermembranes, Phys. Lett. B 180 (1986) 370 [INSPIRE].
J. Khoury, J.-L. Lehners and B.A. Ovrut, Supersymmetric Galileons, Phys. Rev. D 84 (2011) 043521 [arXiv:1103.0003] [INSPIRE].
K. Kamimura and S. Onda, Contractions of AdS brane algebra and superGalileon Lagrangians, J. Math. Phys. 54 (2013) 062503 [arXiv:1303.5506] [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: 1710.02480
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Roest, D., Werkman, P. & Yamada, Y. Internal supersymmetry and small-field Goldstini. J. High Energ. Phys. 2018, 190 (2018). https://doi.org/10.1007/JHEP05(2018)190
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2018)190