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We show that in the quadratic curvature theory of gravity, or simply $R_{mu u} ^2$ gravity, the tree-level unitariy bound (tree unitarity) is violated in the UV region but an analog for $S$-matrix unitarity ($SS^{dagger} = 1$) is satisfied. This theory is renormalizable, and hence the failure of tree unitarity is a counter example of Llewellyn Smiths 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 tree level in the $R_{mu u} ^2$ gravity, demonstrating our new conjecture.
We investigate the ultraviolet (UV) behavior of two-scalar elastic scattering with graviton exchanges in higher curvature gravity theory. In the Einstein gravity, matter scattering is shown not to satisfy tree unitarity at high energy. Among a few po
The infrared behavior of perturbative quantum gravity is studied using the method developed for QED by Faddeev and Kulish. The operator describing the asymptotic dynamics is derived and used to construct an IR-finite S matrix and space of asymptotic
We compute the one-loop divergences in a theory of gravity with Lagrangian of the general form $f(R,R_{mu u}R^{mu u})$, on an Einstein background. We also establish that the one-loop effective action is invariant under a duality that consists of chan
We study the stability of fuzzy S^2 x S^2 x S^2 backgrounds in three different IIB type matrix models with respect to the change of the spins of each S^2 at the two loop level. We find that S^2 x S^2 x S^2 background is metastable and the effective a
We investigate the relation between the $S$-matrix unitarity ($SS^{dagger}=1$) and the renormalizability, in theories with negative norm states. The relation has been confirmed in many theories, such as gauge theories, Einstein gravity and Lifshitz-t