Strong-coupling approach to the quantization of conformal gravity

Abstract

Unlike the Einstein-Hilbert action, conformal gravity is a formally renormalizable theory. However, conformal gravity has nonunitary dipole ghosts when quantized in the weak-coupling approximation. We conjecture that the weak-coupling limit is not a valid one, because of the presence of infrared divergences and the existence of nontrivial Dirac constraints on the physical eigenstates of the theory. We show that the simplest, realistic analog for conformal gravity is higher-derivative Yang-Mills theory. We study its strong-coupling limit and show that its eigenstates are stringlike and that the dipole ghosts are completely eliminated by the gauge constraints. We formulate conformal gravity in the strong-coupling approximation, both in Hamiltonian and Lagrangian forms. Again, there seem to be powerful constraints which eliminate dipole ghosts from the eigenstates of the Hamiltonian and which allow stringlike states. We find ghost confinement. One interpretation, in this picture, is to identify the graviton as a stringlike solution to the Dirac constraints of the conformal group.