Towards a bihamiltonian structure for the double ramification hierarchy

TL;DR

This paper proposes a simple, explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy linked to any homogeneous cohomological field theory, supported by various checks.

Contribution

It introduces a novel explicit conjectural formula for the bihamiltonian structure of the double ramification hierarchy applicable to all homogeneous cohomological field theories.

Findings

Proposed a simple explicit formula for the bihamiltonian structure.

Provided supporting checks validating the conjecture.

Applicable to arbitrary homogeneous cohomological field theories.

Abstract

We propose a remarkably simple and explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy corresponding to an arbitrary homogeneous cohomological field theory. Various checks are presented to support the conjecture.