Abstract:
Conformal symmetry is a natural symmetry in physics since it is the full symmetry of the light cone. If all particles are to get their masses by symmetry breaking then conformal symmetry is the symmetry of the unbroken Lagrangian. Like Yang-Mills theories conformal symmetry has a local extension, namely conformal gravity, a pure metric-based candidate alternative to the non-conformal invariant standard Newton-Einstein theory of gravity. With its dimensionless coupling constant quantum conformal gravity is power counting renormalizable. Since its equations of motion are fourth-order derivative equations conformal gravity has long been thought to possess unacceptable ghost states of negative norm that would violate unitarity. However, on constructing the quantum Hilbert space Bender and Mannheim found that this not to be the case. Conformal gravity is thus offered as a completely consistent and unitary quantum theory of gravity, one that requires neither the extra dimensions nor the supersymmetry of string theory. As formulated via local conformal invariance there is no intrinsic classical gravity, with gravity instead being intrinsically quantum-mechanical, with the observed classical gravity being output rather than input. The contribution of the graviton loops of conformal gravity enables conformal gravity to solve the cosmological constant problem. Like Yang-Mills the potential of conformal gravity contains both a Newtonian term and a linear potential. Together with a quadratic potential that the theory also contains conformal gravity is able to explain the systematics of galactic rotation curves without any need for galactic dark matter. Since all mass is to be dynamical there cannot be a fundamental double-well Higgs potential in the theory. Instead, the Higgs boson is generated dynamically, with the hierarchy problem then being solved.
