Givental Action and Trivialisation of Circle Action

TL;DR

This paper reveals that the Givental group action on genus zero cohomological field theories can be understood through the deformation theory of Batalin--Vilkovisky algebras, linking geometry and homotopical algebra.

Contribution

It establishes that the Givental action corresponds to trivializations of the trivial circle action, unifying geometric and algebraic perspectives.

Findings

Givental action equals trivializations of circle action

Links deformation theory of BV algebras with Givental group

Bridges geometry and homotopical algebra in cohomological field theories

Abstract

In this paper, we show that the Givental group action on genus zero cohomological field theories, also known as formal Frobenius manifolds or hypercommutative algebras, naturally arises in the deformation theory of Batalin--Vilkovisky algebras. We prove that the Givental action is equal to an action of the trivialisations of the trivial circle action. This result relies on the equality of two Lie algebra actions coming from two apparently remote domains: geometry and homotopical algebra.