The Eynard--Orantin recursion for the total ancestor potential

Abstract: It was proved recently that the correlation functions of a semi-simple cohomological field theory satisfy the so called Eynard--Orantin topological recursion. We prove that in the settings of singularity theory, the relations can be expressed in terms of periods integrals and the so called phase forms. In particular, we prove that the Eynard-Orantin recursion is equivalent to $N$ copies of Virasoro constraints for the ancestor potential, which follow easily from the definition of the potential.