Perturbative S-matrix unitarity (S*S=1) in R-mu nu(2) gravity

We show that in the quadratic curvature theory of gravity, or simply R-mu nu(2) gravity, the tree-level unitarity 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 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 R-mu nu(2) gravity, demonstrating our new conjecture.

Automated summary

The study reveals that in the quadratic curvature theory of gravity, the tree-level unitarity bound is violated in the UV region, but the S-matrix unitarity is satisfied. The theory is renormalizable and the failure of tree unitarity acts as a counter example to Llewellyn Smith’s conjecture. A new conjecture is proposed suggesting that S-matrix unitarity and renormalizability share similar conditions, which is demonstrated through matter-graviton scattering in R-mu nu(2) gravity.