Abstract
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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