Gravity and Yang-Mills theory

Abstract

Three of the four forces of Nature are described by quantum Yang–Mills theories with remarkable precision. The fourth force, gravity, is described classically by the Einstein–Hilbert theory. There appears to be an inherent incompatibility between quantum mechanics and the Einstein–Hilbert theory which prevents us from developing a consistent quantum theory of gravity. The Einstein–Hilbert theory is therefore believed to differ greatly from Yang–Mills theory (which does have a sensible quantum mechanical description). It is therefore very surprising that these two theories actually share close perturbative ties. This essay focuses on these ties between Yang–Mills theory and the Einstein–Hilbert theory. We discuss the origin of these ties and their implications for a quantum theory of gravity.