Ghost-free, nonlinear, spin-two, conformal gauge theory

Conformal gravity is examined with the aim of constructing a renormalizable quantum field theory of gravitation. Acting on suggestions of ghost-free, linear conformal gravity, we examine conformal gauge theory. The correct choice of constraints is determined by comparison with the ghost-eliminating constraints of the linear theory. (These are quite different from those introduced previously in conformal gauge theories.) Einstein's field equation appears as the integrability condition for the constraint. Minimal coupling to massless matter preserves local, conformal symmetry.