Renormalization for a non-renormalizable theory: remarks on gravity

We compare the structure of the Dyson Schwinger equations (DSE) for three different situations: the case of a renormalizable field theory, a generic non-renormalizable theory and pure gravity. We use the Hochschild cohomology of the underlying Hopf algebra to formulate the relevant DSEs. Remarkably, it turns out that gravity is much better behaved than a generic non-renormalizable theory with respect to its Hochschild cohomology and discuss some consequences.