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.