# Tautological relations in Hodge field theory

## TL;DR

This paper introduces a Hodge field theory framework that generalizes existing constructions to higher genera, demonstrating that its correlators satisfy all tautological relations, thus unifying and extending prior results.

## Contribution

It develops a new Hodge field theory construction that captures algebraic properties of Gromov-Witten invariants and proves that its correlators satisfy all tautological relations, generalizing previous results.

## Key findings

- Proves Hodge field theory correlators satisfy tautological relations
- Generalizes Barannikov-Kontsevich construction to higher genera
- Provides a conceptual proof replacing technical arguments

## Abstract

We propose a Hodge field theory construction that captures algebraic properties of the reduction of Zwiebach invariants to Gromov-Witten invariants. It generalizes the Barannikov-Kontsevich construction to the case of higher genera correlators with gravitational descendants. We prove the main theorem stating that algebraically defined Hodge field theory correlators satisfy all tautological relations. From this perspective the statement that Barannikov-Kontsevich construction provides a solution of the WDVV equation looks as the simplest particular case of our theorem. Also it generalizes the particular cases of other low-genera tautological relations proven in our earlier works; we replace the old technical proofs by a novel conceptual proof.