Abstract
Lorentz-invariant massive gravity is usually associated with a strong coupling scale Λ3. By including non-trivial effects from the Stückelberg modes, we show that about these vacua, one can push the strong coupling scale to higher values and evade the linear vDVZ-discontinuity. For generic parameters of the theory and generic vacua for the Stückelberg fields, the Λ2-decoupling limit of the theory is well-behaved and free of any ghost or gradient-like instabilities. We also discuss the implications for nonlinear sigma models with Lorentzian target spaces.
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References
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].
D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].
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].
P. Creminelli, A. Nicolis, M. Papucci and E. Trincherini, Ghosts in massive gravity, JHEP 09 (2005) 003 [hep-th/0505147] [INSPIRE].
A.I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett. B 39 (1972) 393 [INSPIRE].
H. van Dam and M.J.G. Veltman, Massive and massless Yang-Mills and gravitational fields, Nucl. Phys. B 22 (1970) 397 [INSPIRE].
V.I. Zakharov, Linearized gravitation theory and the graviton mass, JETP Lett. 12 (1970) 312 [INSPIRE].
C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
S.F. Hassan and R.A. Rosen, Resolving the ghost problem in non-linear massive gravity, Phys. Rev. Lett. 108 (2012) 041101 [arXiv:1106.3344] [INSPIRE].
S.F. Hassan and R.A. Rosen, Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity, JHEP 04 (2012) 123 [arXiv:1111.2070] [INSPIRE].
C. Deffayet, G.R. Dvali, G. Gabadadze and A.I. Vainshtein, Nonperturbative continuity in graviton mass versus perturbative discontinuity, Phys. Rev. D 65 (2002) 044026 [hep-th/0106001] [INSPIRE].
C. de Rham, Massive gravity, Living Rev. Rel. 17 (2014) 7 [arXiv:1401.4173] [INSPIRE].
E. Babichev and C. Deffayet, An introduction to the Vainshtein mechanism, Class. Quant. Grav. 30 (2013) 184001 [arXiv:1304.7240] [INSPIRE].
C. de Rham, A.J. Tolley and S.-Y. Zhou, Non-compact nonlinear σ-models, arXiv:1512.06838 [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Ghost free massive gravity in the Stückelberg language, Phys. Lett. B 711 (2012) 190 [arXiv:1107.3820] [INSPIRE].
I.I. Kogan, S. Mouslopoulos and A. Papazoglou, The m → 0 limit for massive graviton in dS 4 and AdS 4 : how to circumvent the van Dam-Veltman-Zakharov discontinuity, Phys. Lett. B 503 (2001) 173 [hep-th/0011138] [INSPIRE].
M. Porrati, No van Dam-Veltman-Zakharov discontinuity in AdS space, Phys. Lett. B 498 (2001) 92 [hep-th/0011152] [INSPIRE].
A. Karch, E. Katz and L. Randall, Absence of a VVDZ discontinuity in AdS(AdS), JHEP 12 (2001) 016 [hep-th/0106261] [INSPIRE].
M. Porrati, Higgs phenomenon for the graviton in AdS space, Mod. Phys. Lett. A 18 (2003) 1793 [hep-th/0306253] [INSPIRE].
M. Porrati, Massive gravity in AdS and Minkowski backgrounds, in the proceedings of the Deserfest: A celebration of the life and works of Stanley Deser, April 3-5, Ann Arbor, U.S.A. (2004), hep-th/0409172 [INSPIRE].
C. de Rham, G. Gabadadze, L. Heisenberg and D. Pirtskhalava, Nonrenormalization and naturalness in a class of scalar-tensor theories, Phys. Rev. D 87 (2013) 085017 [arXiv:1212.4128] [INSPIRE].
K. Aoki, K.-i. Maeda and R. Namba, Stability of the early universe in bigravity theory, Phys. Rev. D 92 (2015) 044054 [arXiv:1506.04543] [INSPIRE].
C. de Rham et al., Cosmic acceleration and the helicity-0 graviton, Phys. Rev. D 83 (2011) 103516 [arXiv:1010.1780] [INSPIRE].
D. Comelli, F. Nesti and L. Pilo, Nonderivative modified gravity: a classification, JCAP 11 (2014) 018 [arXiv:1407.4991] [INSPIRE].
A. De Felice and S. Mukohyama, Minimal theory of massive gravity, Phys. Lett. B 752 (2016) 302 [arXiv:1506.01594] [INSPIRE].
C. de Rham and G. Gabadadze, Selftuned massive Spin-2, Phys. Lett. B 693 (2010) 334 [arXiv:1006.4367] [INSPIRE].
S.V. Ketov, Nonlinear Sigma model, Scholarpedia 4 (2009) 8508.
S.V. Ketov, Quantum non-linear sigma-models, Springer, Berlin Germany (2000).
W.J. Zakrzewski, Low dimensional sigma models, in the proceedings of the 4th Meeting of the Division of Particles and Fields of the APS, Bristol, U.K. (1989).
L. Brink, P. Di Vecchia and P.S. Howe, A locally supersymmetric and reparametrization invariant action for the spinning string, Phys. Lett. B 65 (1976) 471 [INSPIRE].
S. Deser and B. Zumino, A complete action for the spinning string, Phys. Lett. B 65 (1976) 369 [INSPIRE].
A.M. Polyakov, Interaction of Goldstone particles in two-dimensions. applications to ferromagnets and massive Yang-Mills fields, Phys. Lett. B 59 (1975) 79 [INSPIRE].
Y. Nambu, Duality and hadrodynamics, Notes prepared for the Copenhagen high energy symposium (1970), reprinted in Broken Symmetry: Selected Papers of Y. Nambu, T. Eguchi and K. Nishijima eds., World Scientific, Singapore (1995).
T. Goto, Relativistic quantum mechanics of one-dimensional mechanical continuum and subsidiary condition of dual resonance model, Prog. Theor. Phys. 46 (1971) 1560 [INSPIRE].
O. Hara, On origin and physical meaning of ward-like identity in dual-resonance model, Prog. Theor. Phys. 46 (1971) 1549 [INSPIRE].
K. Becker, M. Becker and J.H. Schwarz, String theory and M-theory: a modern introduction, Cambridge University Press, Camrbidge U.K. (2006).
E. Cremmer and B. Julia, The SO (8) supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
P. Van Nieuwenhuizen, Supergravity, Phys. Rept. 68 (1981) 189 [INSPIRE].
C. De Rham, L. Keltner and A.J. Tolley, Generalized galileon duality, Phys. Rev. D 90 (2014) 024050 [arXiv:1403.3690] [INSPIRE].
M. Gell-Mann and M. Levy, The axial vector current in beta decay, Nuovo Cim. 16 (1960) 705 [INSPIRE].
R.L. Arnowitt, S. Deser and C.W. Misner, The dynamics of general relativity, Gen. Rel. Grav. 40 (2008) 1997 [gr-qc/0405109] [INSPIRE].
L. Berezhiani, G. Chkareuli and G. Gabadadze, Restricted galileons, Phys. Rev. D 88 (2013) 124020 [arXiv:1302.0549] [INSPIRE].
L. Berezhiani, G. Chkareuli, C. de Rham, G. Gabadadze and A.J. Tolley, Mixed galileons and spherically symmetric solutions, Class. Quant. Grav. 30 (2013) 184003 [arXiv:1305.0271] [INSPIRE].
L. Alberte and A. Khmelnitsky, Stability of massive gravity solutions for holographic conductivity, Phys. Rev. D 91 (2015) 046006 [arXiv:1411.3027] [INSPIRE].
L. Alberte and A. Khmelnitsky, Reduced massive gravity with two Stückelberg fields, Phys. Rev. D 88 (2013) 064053 [arXiv:1303.4958] [INSPIRE].
S.F. Hassan, R.A. Rosen and A. Schmidt-May, Ghost-free massive gravity with a general reference metric, JHEP 02 (2012) 026 [arXiv:1109.3230] [INSPIRE].
A. De Felice, A.E. Gumrukcuoglu and S. Mukohyama, Massive gravity: nonlinear instability of the homogeneous and isotropic universe, Phys. Rev. Lett. 109 (2012) 171101 [arXiv:1206.2080] [INSPIRE].
K. Hinterbichler and R.A. Rosen, Interacting spin-2 fields, JHEP 07 (2012) 047 [arXiv:1203.5783] [INSPIRE].
A. Golovnev, On the Hamiltonian analysis of non-linear massive gravity, Phys. Lett. B 707 (2012) 404 [arXiv:1112.2134] [INSPIRE].
S.F. Hassan, A. Schmidt-May and M. von Strauss, Proof of consistency of nonlinear massive gravity in the Stückelberg formulation, Phys. Lett. B 715 (2012) 335 [arXiv:1203.5283] [INSPIRE].
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de Rham, C., Tolley, A.J. & Zhou, SY. The Λ2 limit of massive gravity. J. High Energ. Phys. 2016, 188 (2016). https://doi.org/10.1007/JHEP04(2016)188
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DOI: https://doi.org/10.1007/JHEP04(2016)188