Quantum Gravity in Plebanski Formulation

We present a theory of four-dimensional quantum gravity with massive gravitons which may be essentially renormalizable. In the Plebanski formulation of General Relativity (GR), in which the tetrads, the connection and the curvature are all independent variables (and the usual relations among these quantities are valid only on-shell), we consider a nonperturbative theory of gravity with a nonzero background connection. We predict a tiny value of the graviton mass: m_g\approx 1.8\times 10^{-42} GeV and an extremely small dimensionless coupling constant of the perturbative gravitational interaction: g ~ 10^{-61}. We put forward the idea by H. Isimori on renormalizability of quantum gravity having multi-gravitons with masses m_0, m_1,…, m_{N-1}.