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Bonifacio, James; Hinterbichler, Kurt; Johnson, Laura A.; Joyce, Austin

Shift-symmetric spin-1 theories. (English) Zbl 1423.83050

J. High Energy Phys. 2019, No. 9, Paper No. 29, 32 p. (2019).
Summary: We study interacting massive spin-1 theories in de Sitter (dS) and anti-de Sitter (AdS) space that possess shift symmetries parametrized by (A)dS Killing vectors. We show how they emerge from the massless limit of massive spin-2 theories on (A)dS space. In the case of massive gravity, the corresponding spin-1 theory realizes a symmetry breaking pattern that takes two copies of the (A)dS isometry group down to a diagonal subgroup. By taking the flat space limit of this theory, we find a new symmetry of the decoupling limit of massive gravity in flat space. This symmetry acts on the vector modes, is parametrize by an antisymmetric tensor, and fixes the nonlinear structure of the scalar-vector sector of the decoupling limit.

Cited in 9 Documents

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
81R40 Symmetry breaking in quantum theory

Keywords:

effective field theories; global symmetries; spontaneous symmetry breaking; classical theories of gravity
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References:

[1] S.L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial vector current, Phys. Rev.137 (1965) B1022 [INSPIRE].
[2] S.L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial-vector current. II, Phys. Rev.139 (1965) B1638 [INSPIRE].
[3] 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].
[4] M. Trodden and K. Hinterbichler, Generalizing Galileons, Class. Quant. Grav.28 (2011) 204003 [arXiv:1104.2088] [INSPIRE]. · Zbl 1228.83152
[5] K. Hinterbichler and A. Joyce, Goldstones with extended shift symmetries, Int. J. Mod. Phys.D 23 (2014) 1443001 [arXiv:1404.4047] [INSPIRE]. · Zbl 1315.81093
[6] T. Griffin, K.T. Grosvenor, P. Hořava and Z. Yan, Scalar field theories with polynomial shift symmetries, Commun. Math. Phys.340 (2015) 985 [arXiv:1412.1046] [INSPIRE]. · Zbl 1328.81152 · doi:10.1007/s00220-015-2461-2
[7] C. de Rham and A.J. Tolley, DBI and the Galileon reunited, JCAP05 (2010) 015 [arXiv:1003.5917] [INSPIRE]. · doi:10.1088/1475-7516/2010/05/015
[8] 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].
[9] G. Goon, K. Hinterbichler and M. Trodden, Symmetries for Galileons and DBI scalars on curved space, JCAP07 (2011) 017 [arXiv:1103.5745] [INSPIRE]. · doi:10.1088/1475-7516/2011/07/017
[10] G. Goon, K. Hinterbichler and M. Trodden, A new class of effective field theories from embedded branes, Phys. Rev. Lett.106 (2011) 231102 [arXiv:1103.6029] [INSPIRE]. · doi:10.1103/PhysRevLett.106.231102
[11] G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, Galileons as Wess-Zumino terms, JHEP06 (2012) 004 [arXiv:1203.3191] [INSPIRE]. · doi:10.1007/JHEP06(2012)004
[12] 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]. · doi:10.1103/PhysRevLett.114.221602
[13] C. Cheung et al., On-shell recursion relations for effective field theories, Phys. Rev. Lett.116 (2016) 041601 [arXiv:1509.03309] [INSPIRE].
[14] C. Cheunget al., A periodic table of effective field theories, JHEP02 (2017) 020 [arXiv:1611.03137] [INSPIRE]. · Zbl 1377.81123
[15] C. Cheung et al., Vector effective field theories from soft limits, Phys. Rev. Lett.120 (2018) 261602 [arXiv:1801.01496] [INSPIRE]. · doi:10.1103/PhysRevLett.120.261602
[16] R. Klein, D. Roest and D. Stefanyszyn, Spontaneously broken spacetime symmetries and the role of inessential goldstones, JHEP10 (2017) 051 [arXiv:1709.03525] [INSPIRE]. · Zbl 1383.81111 · doi:10.1007/JHEP10(2017)051
[17] R. Klein, E. Malek, D. Roest and D. Stefanyszyn, No-go theorem for a gauge vector as a spacetime Goldstone mode, Phys. Rev.D 98 (2018) 065001 [arXiv:1806.06862] [INSPIRE].
[18] M.P. Bogers and T. Brauner, Lie-algebraic classification of effective theories with enhanced soft limits, JHEP05 (2018) 076 [arXiv:1803.05359] [INSPIRE]. · Zbl 1391.81139 · doi:10.1007/JHEP05(2018)076
[19] D. Roest, D. Stefanyszyn and P. Werkman, An algebraic classification of exceptional EFTs, arXiv:1903.08222 [INSPIRE]. · Zbl 1421.81080
[20] D. Roest, D. Stefanyszyn and P. Werkman, An algebraic classification of exceptional EFTs part II: supersymmetry, arXiv:1905.05872 [INSPIRE]. · Zbl 1429.81047
[21] J. Bonifacio, K. Hinterbichler, A. Joyce and R.A. Rosen, Shift symmetries in (Anti) de Sitter space, JHEP02 (2019) 178 [arXiv:1812.08167] [INSPIRE]. · Zbl 1411.83062 · doi:10.1007/JHEP02(2019)178
[22] C. De Rham, K. Hinterbichler and L.A. Johnson, On the (A)dS decoupling limits of massive gravity, JHEP09 (2018) 154 [arXiv:1807.08754] [INSPIRE]. · Zbl 1398.83093 · doi:10.1007/JHEP09(2018)154
[23] S. Folkerts, A. Pritzel and N. Wintergerst, On ghosts in theories of self-interacting massive spin-2 particles, arXiv:1107.3157 [INSPIRE].
[24] K. Hinterbichler, Ghost-free derivative interactions for a massive graviton, JHEP10 (2013) 102 [arXiv:1305.7227] [INSPIRE]. · Zbl 1342.83299 · doi:10.1007/JHEP10(2013)102
[25] S. Akagi, Y. Ohara and S. Nojiri, New massive spin two model on a curved spacetime, Phys. Rev.D 90 (2014) 123013 [arXiv:1410.5553] [INSPIRE].
[26] C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett.106 (2011) 231101 [arXiv:1011.1232] [INSPIRE]. · doi:10.1103/PhysRevLett.106.231101
[27] C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli action, Phys. Rev.D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
[28] M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond.A 173 (1939) 211. · Zbl 0023.43004
[29] J. Fang and C. Fronsdal, Elementary particles in a curved space. 5. massive and massless spin-2 fields, Lett. Math. Phys.2 (1978) 391 [INSPIRE].
[30] P.A.M. Dirac, Wave equations in conformal space, Ann. Math.37 (1936) 429. · Zbl 0014.08004 · doi:10.2307/1968455
[31] C. Fronsdal, Singletons and massless, integral spin fields on de Sitter space (Elementary particles in a curved space 7), Phys. Rev.D 20 (1979) 848 [INSPIRE].
[32] C. Burrage, C. de Rham and L. Heisenberg, De Sitter Galileon, JCAP05 (2011) 025 [arXiv:1104.0155] [INSPIRE]. · doi:10.1088/1475-7516/2011/05/025
[33] C. de Rham and S. Renaux-Petel, Massive gravity on de Sitter and unique candidate for partially massless gravity, JCAP01 (2013) 035 [arXiv:1206.3482] [INSPIRE]. · doi:10.1088/1475-7516/2013/01/035
[34] X. Gao, T. Kobayashi, M. Yamaguchi and D. Yoshida, Covariant Stückelberg analysis of de Rham-Gabadadze-Tolley massive gravity with a general fiducial metric, Phys. Rev.D 90 (2014) 124073 [arXiv:1409.3074] [INSPIRE].
[35] X. Gao, Covariant expansion of the gravitational Stückelberg trick, Phys. Rev.D 91 (2015) 094001 [arXiv:1502.07691] [INSPIRE].
[36] K. Hinterbichler, Theoretical aspects of massive gravity, Rev. Mod. Phys.84 (2012) 671 [arXiv:1105.3735] [INSPIRE]. · doi:10.1103/RevModPhys.84.671
[37] C. de Rham, Massive gravity, Living Rev. Rel.17 (2014) 7 [arXiv:1401.4173] [INSPIRE]. · Zbl 1320.83018 · doi:10.12942/lrr-2014-7
[38] S.F. Hassan, R.A. Rosen and A. Schmidt-May, Ghost-free massive gravity with a general reference metric, JHEP02 (2012) 026 [arXiv:1109.3230] [INSPIRE]. · Zbl 1309.83084 · doi:10.1007/JHEP02(2012)026
[39] G. Gabadadze, K. Hinterbichler, D. Pirtskhalava and Y. Shang, Potential for general relativity and its geometry, Phys. Rev.D 88 (2013) 084003 [arXiv:1307.2245] [INSPIRE].
[40] N.A. Ondo and A.J. Tolley, Complete decoupling limit of ghost-free massive gravity, JHEP11 (2013) 059 [arXiv:1307.4769] [INSPIRE]. · Zbl 1342.83223 · doi:10.1007/JHEP11(2013)059
[41] C. de Rham and G. Gabadadze, Selftuned massive spin-2, Phys. Lett.B 693 (2010) 334 [arXiv:1006.4367] [INSPIRE].
[42] K. Koyama, G. Niz and G. Tasinato, The self-accelerating universe with vectors in massive gravity, JHEP12 (2011) 065 [arXiv:1110.2618] [INSPIRE]. · Zbl 1306.83065 · doi:10.1007/JHEP12(2011)065
[43] G. Tasinato, K. Koyama and G. Niz, Vector instabilities and self-acceleration in the decoupling limit of massive gravity, Phys. Rev.D 87 (2013) 064029 [arXiv:1210.3627] [INSPIRE]. · Zbl 1277.83093
[44] S. Yu, Superluminal vector in ghost-free massive gravity, JHEP09 (2014) 019 [arXiv:1310.6469] [INSPIRE]. · Zbl 1333.83031 · doi:10.1007/JHEP09(2014)019
[45] C. Deffayet and J.-W. Rombouts, Ghosts, strong coupling and accidental symmetries in massive gravity, Phys. Rev.D 72 (2005) 044003 [gr-qc/0505134] [INSPIRE].
[46] N. Arkani-Hamed, H. Georgi and M.D. Schwartz, Effective field theory for massive gravitons and gravity in theory space, Annals Phys.305 (2003) 96 [hep-th/0210184] [INSPIRE]. · Zbl 1022.81035 · doi:10.1016/S0003-4916(03)00068-X
[47] J. Bonifacio, K. Hinterbichler and L.A. Johnson, Pseudolinear spin-2 interactions, Phys. Rev.D 99 (2019) 024037 [arXiv:1806.00483] [INSPIRE].
[48] G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys.B 633 (2002) 3 [hep-th/0111246] [INSPIRE]. · Zbl 0995.81054
[49] E.A. Ivanov and V.I. Ogievetsky, Gauge theories as theories of spontaneous breakdown, Lett. Math. Phys.1 (1976) 309 [INSPIRE]. · doi:10.1007/BF00398486
[50] G. Goon, A. Joyce and M. Trodden, Spontaneously broken gauge theories and the coset construction, Phys. Rev.D 90 (2014) 025022 [arXiv:1405.5532] [INSPIRE].
[51] G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, Einstein gravity, massive gravity, multi-gravity and nonlinear realizations, JHEP07 (2015) 101 [arXiv:1412.6098] [INSPIRE]. · Zbl 1388.83583 · doi:10.1007/JHEP07(2015)101
[52] G. Tasinato, Cosmic acceleration from abelian symmetry breaking, JHEP04 (2014) 067 [arXiv:1402.6450] [INSPIRE]. · Zbl 1333.83281 · doi:10.1007/JHEP04(2014)067
[53] L. Heisenberg, Generalization of the Proca action, JCAP05 (2014) 015 [arXiv:1402.7026] [INSPIRE]. · doi:10.1088/1475-7516/2014/05/015
[54] M. Hull, K. Koyama and G. Tasinato, A Higgs mechanism for vector galileons, JHEP03 (2015) 154 [arXiv:1408.6871] [INSPIRE]. · Zbl 1388.83922 · doi:10.1007/JHEP03(2015)154
[55] G. Tasinato, A small cosmological constant from Abelian symmetry breaking, Class. Quant. Grav.31 (2014) 225004 [arXiv:1404.4883] [INSPIRE]. · Zbl 1309.83097 · doi:10.1088/0264-9381/31/22/225004
[56] E. Allys, P. Peter and Y. Rodriguez, Generalized Proca action for an Abelian vector field, JCAP02 (2016) 004 [arXiv:1511.03101] [INSPIRE]. · doi:10.1088/1475-7516/2016/02/004
[57] M. Hull, K. Koyama and G. Tasinato, Covariantized vector Galileons, Phys. Rev.D 93 (2016) 064012 [arXiv:1510.07029] [INSPIRE]. · Zbl 1388.83922
[58] F. Charmchi, Z. Haghani, S. Shahidi and L. Shahkarami, One-loop corrections to vector Galileon theory, Phys. Rev.D 93 (2016) 124044 [arXiv:1511.07034] [INSPIRE].
[59] J. Beltran Jimenez and L. Heisenberg, Derivative self-interactions for a massive vector field, Phys. Lett.B 757 (2016) 405 [arXiv:1602.03410] [INSPIRE]. · Zbl 1360.83046
[60] E. Allys, J.P. Beltran Almeida, P. Peter and Y. Rodríguez, On the 4D generalized Proca action for an Abelian vector field, JCAP09 (2016) 026 [arXiv:1605.08355] [INSPIRE].
[61] L. Heisenberg, Generalised Proca Theories, in the proceedings of the 52ndRencontres de Moriond on Gravitation (Moriond Gravitation 2017), March 25-April 1, La Thuile, Italy (2017), arXiv:1705.05387 [INSPIRE].
[62] V. Errasti Díez, B. Gording, J.A. Méndez-Zavaleta and A. Schmidt-May, The complete theory of Maxwell and Proca fields, arXiv:1905.06967 [INSPIRE].
[63] V. Errasti Díez, B. Gording, J.A. Méndez-Zavaleta and A. Schmidt-May, The Maxwell-Proca theory: definition and construction, arXiv:1905.06968 [INSPIRE].
[64] A. Gallego Cadavid and Y. Rodriguez, A systematic procedure to build the beyond generalized Proca field theory, arXiv:1905.10664 [INSPIRE]. · Zbl 1434.70067
[65] J. Beltrán Jiménez, C. de Rham and L. Heisenberg, Generalized Proca and its constraint algebra, arXiv:1906.04805 [INSPIRE]. · Zbl 1435.70045
[66] E. Joung and K. Mkrtchyan, Partially-massless higher-spin algebras and their finite-dimensional truncations, JHEP01 (2016) 003 [arXiv:1508.07332] [INSPIRE]. · Zbl 1388.83593 · doi:10.1007/JHEP01(2016)003
[67] B. Bellazzini, F. Riva, J. Serra and F. Sgarlata, Massive higher spins: effective theory and consistency, arXiv:1903.08664 [INSPIRE]. · Zbl 1427.81068
[68] J.J. Bonifacio, Aspects of massive spin-2 effective field theories, Ph.D. thesis, Oxford University, Oxford, U.K. (2017).
[69] J. Bonifacio and K. Hinterbichler, Bounds on amplitudes in effective theories with massive spinning particles, Phys. Rev.D 98 (2018) 045003 [arXiv:1804.08686] [INSPIRE].
[70] M.A. Luty, M. Porrati and R. Rattazzi, Strong interactions and stability in the DGP model, JHEP09 (2003) 029 [hep-th/0303116] [INSPIRE]. · doi:10.1088/1126-6708/2003/09/029
[71] A. Nicolis and R. Rattazzi, Classical and quantum consistency of the DGP model, JHEP06 (2004) 059 [hep-th/0404159] [INSPIRE]. · doi:10.1088/1126-6708/2004/06/059
[72] G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, Aspects of Galileon non-renormalization, JHEP11 (2016) 100 [arXiv:1606.02295] [INSPIRE]. · Zbl 1390.83279 · doi:10.1007/JHEP11(2016)100
[73] A. Folacci, BRST quantization of the massless minimally coupled scalar field in de Sitter space: Zero modes, euclideanization and quantization, Phys. Rev.D 46 (1992) 2553 [arXiv:0911.2064] [INSPIRE].
[74] S.P. Miao, N.C. Tsamis and R.P. Woodard, De Sitter breaking through infrared divergences, J. Math. Phys.51 (2010) 072503 [arXiv:1002.4037] [INSPIRE]. · Zbl 1311.81190
[75] S. Garcia-Saenz, J. Kang and R. Penco, Gauged Galileons, JHEP07 (2019) 081 [arXiv:1905.05190] [INSPIRE]. · Zbl 1422.81144
[76] H. Elvang, M. Hadjiantonis, C.R.T. Jones and S. Paranjape, Soft bootstrap and supersymmetry, JHEP01 (2019) 195 [arXiv:1806.06079] [INSPIRE]. · Zbl 1409.81146 · doi:10.1007/JHEP01(2019)195
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