Quantum master equation and Hodge correlators

We give a generalization of Goncharov's Hodge correlator twistor connection. Our generalized version is a connection 1-form with values in a DG Lie algebra of uni-trivalent graphs which may have loops and satisfies some Maurer--Cartan equation. This connection and the Maurer--Cartan equation can be viewed as an arithmetic analogue of effective action and quantum master equation respectively in non-acyclic Chern--Simons perturbation theory associated with the trivial local system.