We show that in the quadratic curvature theory of gravity, or simply Rμν2 gravity, the tree-level unitarity bound (tree unitarity) is violated in the UV region but an analog for S-matrix unitarity (SS† = 1) 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 S-matrix unitarity gives the same conditions as renormalizability. We verify that S-matrix unitarity holds in the matter-graviton scattering at the tree level in the Rμν2 gravity, demonstrating our new conjecture.

中文翻译：

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Rμν2 引力中的微扰 S 矩阵酉性 (S†S = 1)

我们证明了在引力的二次曲率理论中，或者简单地说Rμν2重力，在 UV 区域中违反了树级统一性界限（树统一性），但类似于小号- 矩阵单一性(小号小号† = 1)很满意。这个理论是可重整的，因此树的单一性的失败是卢埃林·史密斯关于它们之间关系的猜想的一个反例。我们最近提出了一个新的猜想小号-matrix unitarity 给出与可重整性相同的条件。我们验证小号-矩阵的单一性在树级别的物质-引力子散射中成立Rμν2重力，证明了我们的新猜想。