Abstract
The consistency of the EFT of two interacting spin-2 fields is checked by applying forward limit positivity bounds on the scattering amplitudes to exclude the region of parameter space devoid of a standard UV completion. We focus on two classes of theories that have the highest possible EFT cutoff, namely those theories modelled on ghost-free interacting theories of a single massive spin-2 field. We find that the very existence of interactions between the spin-2 fields implies more stringent bounds on all the parameters of the EFT, even on the spin-2 self-interactions. This arises for two reasons. First, with every new field included in the low-energy EFT, comes the ‘knowledge’ of an extra pole to be subtracted, hence strengthening the positivity bounds. Second, while adding new fields increases the number of free parameters from the new interactions, this is rapidly overcome by the increased number of positivity bounds for different possible scattering processes. We also discuss how positivity bounds appear to favour relations between operators that effectively raise the cutoff of the EFT.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Alberte, C. de Rham, A. Momeni, J. Rumbutis and A.J. Tolley, EFT of Interacting Spin-2 Fields, JHEP 01 (2020) 131 [arXiv:1910.05285] [INSPIRE].
K. Hinterbichler and R.A. Rosen, Interacting Spin-2 Fields, JHEP 07 (2012) 047 [arXiv:1203.5783] [INSPIRE].
J.H.C. Scargill, J. Noller and P.G. Ferreira, Cycles of interactions in multi-gravity theories, JHEP 12 (2014) 160 [arXiv:1410.7774] [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.B. Giddings and R.A. Porto, The Gravitational S-matrix, Phys. Rev. D 81 (2010) 025002 [arXiv:0908.0004] [INSPIRE].
T.N. Pham and T.N. Truong, Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation, Phys. Rev. D 31 (1985) 3027 [INSPIRE].
B. Ananthanarayan, D. Toublan and G. Wanders, Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints, Phys. Rev. D 51 (1995) 1093 [hep-ph/9410302] [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].
C. Cheung and G.N. Remmen, Positive Signs in Massive Gravity, JHEP 04 (2016) 002 [arXiv:1601.04068] [INSPIRE].
C. de Rham, S. Melville and A.J. Tolley, Improved Positivity Bounds and Massive Gravity, JHEP 04 (2018) 083 [arXiv:1710.09611] [INSPIRE].
J. Bonifacio, K. Hinterbichler and R.A. Rosen, Positivity constraints for pseudolinear massive spin-2 and vector Galileons, Phys. Rev. D 94 (2016) 104001 [arXiv:1607.06084] [INSPIRE].
B. Bellazzini, F. Riva, J. Serra and F. Sgarlata, Beyond Positivity Bounds and the Fate of Massive Gravity, Phys. Rev. Lett. 120 (2018) 161101 [arXiv:1710.02539] [INSPIRE].
C. Cheung and G.N. Remmen, Positivity of Curvature-Squared Corrections in Gravity, Phys. Rev. Lett. 118 (2017) 051601 [arXiv:1608.02942] [INSPIRE].
B. Bellazzini, C. Cheung and G.N. Remmen, Quantum Gravity Constraints from Unitarity and Analyticity, Phys. Rev. D 93 (2016) 064076 [arXiv:1509.00851] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity bounds for scalar field theories, Phys. Rev. D 96 (2017) 081702 [arXiv:1702.06134] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, UV complete me: Positivity Bounds for Particles with Spin, JHEP 03 (2018) 011 [arXiv:1706.02712] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Massive Galileon Positivity Bounds, JHEP 09 (2017) 072 [arXiv:1702.08577] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity Bounds for Massive Spin-1 and Spin-2 Fields, JHEP 03 (2019) 182 [arXiv:1804.10624] [INSPIRE].
C. Zhang and S.-Y. Zhou, Positivity bounds on vector boson scattering at the LHC, Phys. Rev. D 100 (2019) 095003 [arXiv:1808.00010] [INSPIRE].
Q. Bi, C. Zhang and S.-Y. Zhou, Positivity constraints on aQGC: carving out the physical parameter space, JHEP 06 (2019) 137 [arXiv:1902.08977] [INSPIRE].
C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli Action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
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].
P. Creminelli, A. Nicolis, M. Papucci and E. Trincherini, Ghosts in massive gravity, JHEP 09 (2005) 003 [hep-th/0505147] [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].
M. Fasiello and A.J. Tolley, Cosmological Stability Bound in Massive Gravity and Bigravity, JCAP 12 (2013) 002 [arXiv:1308.1647] [INSPIRE].
N.A. Ondo and A.J. Tolley, Complete Decoupling Limit of Ghost-free Massive Gravity, JHEP 11 (2013) 059 [arXiv:1307.4769] [INSPIRE].
J. Noller and J.H.C. Scargill, The decoupling limit of Multi-Gravity: Multi-Galileons, Dualities and More, JHEP 05 (2015) 034 [arXiv:1503.02700] [INSPIRE].
J.H.C. Scargill and J. Noller, Strong-coupling scales and the graph structure of multi-gravity theories, JHEP 01 (2016) 029 [arXiv:1511.02877] [INSPIRE].
C. de Rham, A. Matas and A.J. Tolley, Deconstructing Dimensions and Massive Gravity, Class. Quant. Grav. 31 (2014) 025004 [arXiv:1308.4136] [INSPIRE].
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 [INSPIRE].
B. Bellazzini, Softness and amplitudes’ positivity for spinning particles, JHEP 02 (2017) 034 [arXiv:1605.06111] [INSPIRE].
C. de Rham, Massive Gravity, Living Rev. Rel. 17 (2014) 7 [arXiv:1401.4173] [INSPIRE].
M. Froissart, Asymptotic behavior and subtractions in the Mandelstam representation, Phys. Rev. 123 (1961) 1053 [INSPIRE].
A. Martin, Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1., Nuovo Cim. A 42 (1965) 930 [INSPIRE].
Y.S. Jin and A. Martin, Number of Subtractions in Fixed-Transfer Dispersion Relations, Phys. Rev. 135 (1964) B1375 [INSPIRE].
C. de Rham and A.J. Tolley, The Speed of Gravity, arXiv:1909.00881 [INSPIRE].
L. Keltner and A.J. Tolley, UV properties of Galileons: Spectral Densities, arXiv:1502.05706 [INSPIRE].
X.O. Camanho, G. Lucena Gómez and R. Rahman, Causality Constraints on Massive Gravity, Phys. Rev. D 96 (2017) 084007 [arXiv:1610.02033] [INSPIRE].
K. Hinterbichler, A. Joyce and R.A. Rosen, Massive Spin-2 Scattering and Asymptotic Superluminality, JHEP 03 (2018) 051 [arXiv:1708.05716] [INSPIRE].
J. Bonifacio, K. Hinterbichler, A. Joyce and R.A. Rosen, Massive and Massless Spin-2 Scattering and Asymptotic Superluminality, JHEP 06 (2018) 075 [arXiv:1712.10020] [INSPIRE].
K. Hinterbichler, A. Joyce and R.A. Rosen, Eikonal scattering and asymptotic superluminality of massless higher spin fields, Phys. Rev. D 97 (2018) 125019 [arXiv:1712.10021] [INSPIRE].
E.P. Wigner, Lower Limit for the Energy Derivative of the Scattering Phase Shift, Phys. Rev. 98 (1955) 145 [INSPIRE].
N. Arkani-Hamed and M.D. Schwartz, Discrete gravitational dimensions, Phys. Rev. D 69 (2004) 104001 [hep-th/0302110] [INSPIRE].
M.D. Schwartz, Constructing gravitational dimensions, Phys. Rev. D 68 (2003) 024029 [hep-th/0303114] [INSPIRE].
C. Deffayet and J. Mourad, Multigravity from a discrete extra dimension, Phys. Lett. B 589 (2004) 48 [hep-th/0311124] [INSPIRE].
C. Deffayet and J. Mourad, Deconstruction of gravity, Int. J. Theor. Phys. 44 (2005) 1743 [INSPIRE].
J. Bonifacio and K. Hinterbichler, Unitarization from Geometry, JHEP 12 (2019) 165 [arXiv:1910.04767] [INSPIRE].
C. Bachas and I. Lavdas, Quantum Gates to other Universes, Fortsch. Phys. 66 (2018) 1700096 [arXiv:1711.11372] [INSPIRE].
C. Bachas and I. Lavdas, Massive Anti-de Sitter Gravity from String Theory, JHEP 11 (2018) 003 [arXiv:1807.00591] [INSPIRE].
C. Bachas, Massive AdS Supergravitons and Holography, JHEP 06 (2019) 073 [arXiv:1905.05039] [INSPIRE].
C. De Rham, L. Heisenberg and A.J. Tolley, Spin-2 fields and the weak gravity conjecture, Phys. Rev. D 100 (2019) 104033 [arXiv:1812.01012] [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: 1910.11799
Rights and permissions
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.
About this article
Cite this article
Alberte, L., de Rham, C., Momeni, A. et al. Positivity constraints on interacting spin-2 fields. J. High Energ. Phys. 2020, 97 (2020). https://doi.org/10.1007/JHEP03(2020)097
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2020)097