A previously published covariant decomposition of the Levi-Civita tensor has demonstrated the strong mathematical parallel between gravity and $N=2$ Yang-Mills theory. We use this to argue that the an $R^2$ type Lagrangian has a stable vacuum of lower energy than the perturbative vacuum. Using a Lagrangian in this form instead of the more conventional Hilbert-Einstein Lagrangian allows us to use the Clairaut-based formalism published by one of us previously to handle gravitys topological degrees of of freedom. We study the effect on second quantisation and discuss the effects on, and of, the particle spectrum.
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