The master relation for polynomiality and equivalences of integrable systems

TL;DR

This paper proves a master relation in the tautological ring of moduli spaces, revealing polynomial properties and equivalences between integrable hierarchies derived from cohomological field theories and double ramification hierarchies.

Contribution

It establishes a fundamental master relation that links polynomiality and equivalences of integrable systems in algebraic geometry.

Findings

Proves the master relation in the tautological ring.

Shows polynomial properties of Dubrovin-Zhang hierarchies.

Establishes equivalences to double ramification hierarchies.

Abstract

We prove the so-called master relation in the tautological ring of the moduli space of curves that implies polynomial properties of the Dubrovin-Zhang hierarchies associated to different versions of cohomological field theories as well as their equivalences to the corresponding double ramification hierarchies.