S-matrix Unitarity toward UV Completion

Einstein gravity is not renormalizable and does not hold perturbative unitarity at high energy. This is the main reason why the construction of quantum gravity is difficult. A conjecture was proposed by Llewellyn Smith, "renormalizablility and tree-unitarity at high energy give the same conditions for theories". This conjecture would be important because it shows that, if a theory is constructed s.t. unitarity is satisfied, renormalizablility holds automatically, and vice versa.
Unfortunately, a counterexample was pointed out. If a theory involves higher derivatives, there exists a theory which is renormalizable but does not satisfy tree-unitarity. A candidate of quantum gravity, the quadratic gravity (R_{\mu\nu}^2 gravity), is one of the examples. Therefore, Llewellyn Smith's conjecture would not be useful for the discussion of quantum gravity. Then, we introduce a new conjecture, "renormalizablility and S-matrix unitarity (or often called pseudo-unitarity) at high energy give the same conditions for theories".
In this talk, Llewellyn Smith's conjecture and our contribution to it will be explained. Then, our new conjecture will be introduced. Finally, it will be shown that our conjecture works well even in theories with higher derivatives.