$S$
          -matrix unitarity and renormalizability in higher-derivative theories

Abe, Yasuyuki; Inami, Takeo; Izumi, Keisuke; Kitamura, Tomotaka; Noumi, Toshifumi

doi:10.1093/ptep/ptz084

Cited by 9 publications

(11 citation statements)

References 29 publications

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“…We suggested in Ref. [11] that S-matrix unitarity can be a guideline to renormalizability, and we have shown in this letter that it is true in gravitational theory. If a kinetic term in the action is degenerate, such as that in gauge theory, because the power counting theorem does not work, the proof of renormalizability is hard.…”

Section: Discussionmentioning

confidence: 67%

“…Quadratic curvature gravity, or simply R 2 µν gravity, is a renormalizable theory [10], but it contains negative norm states of massive graviton and hence the unitarity is violated. We have pointed out that the unitarity bound and the S-matrix unitarity (SS † = 1) are two separate notions [11]. The former often fails in theories containing negative norm states, but the latter provides useful conditions on the UV behavior of a wide class of theories.…”

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confidence: 99%

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Perturbative S-matrix unitarity (S†S = 1) in Rμν2 gravity

2021

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We show that in the quadratic curvature theory of gravity, or simply [Formula: see text] gravity, the tree-level unitarity bound (tree unitarity) is violated in the UV region but an analog for [Formula: see text]-matrix unitarity [Formula: see text] is satisfied. This theory is renormalizable, and hence the failure of tree unitarity is a counter example of Llewellyn Smith’s conjecture on the relation between them. We have recently proposed a new conjecture that [Formula: see text]-matrix unitarity gives the same conditions as renormalizability. We verify that [Formula: see text]-matrix unitarity holds in the matter-graviton scattering at the tree level in the [Formula: see text] gravity, demonstrating our new conjecture.

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Section: Discussionmentioning

confidence: 67%

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confidence: 99%

Perturbative S-matrix unitarity (S†S = 1) in Rμν2 gravity

2021

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“…A similar situation should hold for the S-matrix unitarity. This expectation has been verified at tree level in scalar field theories with higher-order derivatives [13]. In this paper, we focus on the S-matrix unitarity for matter-graviton scattering amplitudes at the tree-level (figure 3) in R 2 µν gravity.…”

Section: Jhep03(2023)213mentioning

confidence: 81%

“…The tree unitarity fails for QFT with higher derivative kinetic terms, including Lee-Wick type QFT [9,10] and R 2 µν gravity [11,12], because of negative norm field (ghost). The tree unitarity can be extended to perturbative S-matrix unitarity (SS † = 1) for higher-derivative QFT [13,14].…”

Section: Introductionmentioning

confidence: 99%

High-energy properties of the graviton scattering in quadratic gravity

Abe

Inami

Izumi

2023

J. High Energ. Phys.

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We obtain the matter-graviton scattering amplitude in the gravitational theory of quadratic curvature, which has $$ {R}_{\mu \nu}^2 $$ R μν 2 term in the action. Unitarity bound is not satisfied because of the existence of negative norm states, while an analog of unitarity bound for S-matrix unitarity holds due to the cancelation among the positive norm states and negative norm ones in the unitarity summation in the optical theorem. The violation of unitarity bound is a counter example of Llewellyn Smith’s conjecture on the relation between tree-level unitarity and renormalizability. We have recently proposed a new conjecture that an analog of the unitarity bound for S-matrix unitarity gives the equivalent conditions to those for renormalizability. We show that the gravitational theory of quadratic curvature is a nontrivial example consistent with our conjecture.

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“…It would be interesting to see what happens for the scattering amplitudes involving gravitons in the external lines. (We are now analyzing a higher-order derivative scalar-field model that is an analog to R 2 gravity [25]. )…”

Section: Discussionmentioning

confidence: 99%

Matter scattering in $R_{μν}^2$ gravity and unitarity

Abe,

Inami,

Izumi

et al. 2017

Preprint

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We investigate the ultraviolet (UV) behavior of two-scalar elastic scattering with graviton exchanges in higher-curvature gravity theory. In Einstein gravity, matter scattering is shown not to satisfy the unitarity bound at tree level at high energy. Among some of the possible directions for the UV completion of Einstein gravity, such as string theory, modied gravity, and inclusion of high-mass/high-spin states, we take R 2 µν gravity coupled to matter. We show that matter scattering with graviton interactions satises the unitarity bound at high energy, even with negative norm states due to the higher-order derivatives of metric components. The difference in the unitarity property of these two gravity theories is probably connected to that in another UV property, namely, the renormalizability property of the two.

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$S$ -matrix unitarity and renormalizability in higher-derivative theories

Cited by 9 publications

References 29 publications

Perturbative S-matrix unitarity (S†S = 1) in Rμν2 gravity

Perturbative S-matrix unitarity (S†S = 1) in Rμν2 gravity

High-energy properties of the graviton scattering in quadratic gravity

Matter scattering in $R_{μν}^2$ gravity and unitarity

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