Gravitational positivity bounds
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Springer
Received: August 17, 2020 Accepted: October 2, 2020 Published: November 11, 2020
Gravitational positivity bounds
a
Department of Physics, Kobe University, Kobe 657-8501, Japan b Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan c Division of Particle and Astrophysical Science, Graduate School of Science, Nagoya University, Aichi 464-8602, Japan
E-mail: [email protected], [email protected], [email protected] Abstract: We study the validity of positivity bounds in the presence of a massless graviton, assuming the Regge behavior of the amplitude. Under this assumption, the problematic t-channel pole is canceled with the UV integral of the imaginary part of the amplitude in the dispersion relation, which gives rise to finite corrections to the positivity bounds. We find that low-energy effective field theories (EFT) with “wrong” sign are generically allowed. The allowed amount of the positivity violation is determined by the Regge behavior. −2 0 This violation is suppressed by Mpl α where α0 is the scale of Reggeization. This implies that the positivity bounds can be applied only when the cutoff scale of EFT is much lower than the scale of Reggeization. We then obtain the positivity bounds on scalar-tensor EFT at one-loop level. Implications of our results on the degenerate higher-order scalar-tensor (DHOST) theory are also discussed. Keywords: Effective Field Theories, Scattering Amplitudes ArXiv ePrint: 2007.15009
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)054
JHEP11(2020)054
Junsei Tokuda,a Katsuki Aokib and Shin’ichi Hiranoc
Contents 1 Introduction
1
2 Review: positivity bounds for scalar theories without gravity
3 6 6 7 9 13
4 Bounds on scalar-tensor EFT 4.1 Frame-independence: example 4.2 Ghost-freeness v.s. EFT point of view 4.3 General action 4.4 Positivity bounds on scalar-tensor EFT
15 15 17 18 21
5 Application to phenomenological models
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6 Conclusion and discussions
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A Extension to the positivity with t-derivative A.1 For scalar theories without gravity A.2 Cancellation of graviton t-channel pole and approximate positivity
29 29 30
B Sub-leading correction: sample calculation
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C One-loop corrections
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D Loops, improved positivity, and the renormalization scale
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E Inclusion of Rφ
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1
Introduction
It is well known that not every consistent-looking low-energy effective field theories (EFT) could be embedded into standard ultraviolet (UV) completions respecting some desired properties such as unitarity and causality. For non-gravitational theories, there is a clean argument that certain combinations of the EFT coefficients of higher-derivative corrections
–1–
JHEP11(2020)054
3 Positivity bounds in the presence of gravity 3.1 Unavoidable problems caused by gravitons 3.2 Violation of strict positivity and the Regge behavior 3.3 An example: superstring amplitude 3.4 Bound on negativity and the approxim
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