The Eynard--Orantin recursion for the total ancestor potential

TL;DR

This paper demonstrates that in singularity theory, the Eynard--Orantin recursion can be expressed via period integrals and phase forms, and is equivalent to multiple Virasoro constraints for the ancestor potential.

Contribution

It establishes the equivalence between Eynard--Orantin recursion and Virasoro constraints in the context of singularity theory, extending previous results to this setting.

Findings

Eynard--Orantin recursion expressed through periods and phase forms

Equivalence of recursion to N copies of Virasoro constraints

Simplification of relations in singularity theory

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.