Abstract
Non-linear realizations of spacetime symmetries can be obtained by a generalization of the coset construction valid for internal ones. The physical equivalence of different representations for spacetime symmetries is not obvious, since their relation involves not only a redefinition of the fields but also a field-dependent change of coordinates. A simple and relevant spacetime symmetry is obtained by the contraction of the 4D conformal group that leads to the Galileon group. We analyze two non-linear realizations of this group, focusing in particular on the propagation of signals around non-trivial backgrounds. The aperture of the lightcone is in general different in the two representations and in particular a free (luminal) massless scalar is mapped in a Galileon theory which admits superluminal propagation. We show that in this theory, if we consider backgrounds that vanish at infinity, there is no asymptotic effect: the displacement of the trajectory integrates to zero, as can be expected since the S-matrix is trivial. Regarding local measurements, we show that the puzzle is solved taking into account that a local coupling with fixed sources in one theory is mapped into a non-local coupling and we show that this effect compensates the different lightcone. Therefore the two theories have a different notion of locality. The same applies to the different non-linear realizations of the conformal group and we study the particular case of a cosmologically interesting background: the Galilean Genesis scenarios.
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].
E.A. Ivanov and V.I. Ogievetsky, The inverse Higgs phenomenon in nonlinear realizations, Teor. Mat. Fiz. 25 (1975) 164 [INSPIRE].
S. Endlich, A. Nicolis and R. Penco, Ultraviolet completion without symmetry restoration, Phys. Rev. D 89 (2014) 065006 [arXiv:1311.6491] [INSPIRE].
T. Brauner and H. Watanabe, Spontaneous breaking of spacetime symmetries and the inverse Higgs effect, Phys. Rev. D 89 (2014) 085004 [arXiv:1401.5596] [INSPIRE].
A. Salam and J.A. Strathdee, Nonlinear realizations. 2. Conformal symmetry, Phys. Rev. 184 (1969) 1760 [INSPIRE].
C.J. Isham, A. Salam and J.A. Strathdee, Nonlinear realizations of space-time symmetries. Scalar and tensor gravity, Annals Phys. 62 (1971) 98 [INSPIRE].
D.V. Volkov, Phenomenological Lagrangians, Fiz. Elem. Chast. Atom. Yadra 4 (1973) 3 [INSPIRE].
P. Creminelli, M. Serone and E. Trincherini, Non-linear representations of the conformal group and mapping of Galileons, JHEP 10 (2013) 040 [arXiv:1306.2946] [INSPIRE].
S. Bellucci, E. Ivanov and S. Krivonos, AdS/CFT equivalence transformation, Phys. Rev. D 66 (2002) 086001 [Erratum ibid. D 67 (2003) 049901] [hep-th/0206126] [INSPIRE].
G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, Galileons as Wess-Zumino terms, JHEP 06 (2012) 004 [arXiv:1203.3191] [INSPIRE].
K. Kamimura and S. Onda, Contractions of AdS brane algebra and super-Galileon Lagrangians, J. Math. Phys. 54 (2013) 062503 [arXiv:1303.5506] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197] [INSPIRE].
C. de Rham and A.J. Tolley, DBI and the Galileon reunited, JCAP 05 (2010) 015 [arXiv:1003.5917] [INSPIRE].
C. de Rham, M. Fasiello and A.J. Tolley, Galileon duality, Phys. Lett. B 733 (2014) 46 [arXiv:1308.2702] [INSPIRE].
T.L. Curtright and D.B. Fairlie, A Galileon primer, arXiv:1212.6972 [INSPIRE].
G.R. Dvali, G. Gabadadze and M. Porrati, 4D gravity on a brane in 5D Minkowski space, Phys. Lett. B 485 (2000) 208 [hep-th/0005016] [INSPIRE].
P. Creminelli, A. Nicolis and E. Trincherini, Galilean genesis: an alternative to inflation, JCAP 11 (2010) 021 [arXiv:1007.0027] [INSPIRE].
K. Hinterbichler, A. Joyce, J. Khoury and G.E.J. Miller, Dirac-Born-Infeld genesis: an improved violation of the null energy condition, Phys. Rev. Lett. 110 (2013) 241303 [arXiv:1212.3607] [INSPIRE].
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, Energy’s and amplitudes’ positivity, JHEP 05 (2010) 095 [Erratum ibid. 11 (2011) 128] [arXiv:0912.4258] [INSPIRE].
A. Nicolis and R. Rattazzi, Classical and quantum consistency of the DGP model, JHEP 06 (2004) 059 [hep-th/0404159] [INSPIRE].
K. Hinterbichler, A. Joyce, J. Khoury and G.E.J. Miller, DBI realizations of the pseudo-conformal universe and Galilean genesis scenarios, JCAP 12 (2012) 030 [arXiv:1209.5742] [INSPIRE].
C. De Rham, L. Keltner and A.J. Tolley, Generalized Galileon duality, Phys. Rev. D 90 (2014) 024050 [arXiv:1403.3690] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R.A. Rosen, More on gapped Goldstones at finite density: more gapped Goldstones, JHEP 11 (2013) 055 [arXiv:1306.1240] [INSPIRE].
A. Nicolis, R. Penco and R.A. Rosen, Relativistic fluids, superfluids, solids and supersolids from a coset construction, Phys. Rev. D 89 (2014) 045002 [arXiv:1307.0517] [INSPIRE].
G. Goon, K. Hinterbichler and M. Trodden, Symmetries for Galileons and DBI scalars on curved space, JCAP 07 (2011) 017 [arXiv:1103.5745] [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: 1403.3095
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
Creminelli, P., Serone, M., Trevisan, G. et al. Inequivalence of coset constructions for spacetime symmetries. J. High Energ. Phys. 2015, 37 (2015). https://doi.org/10.1007/JHEP02(2015)037
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2015)037