A perturbative algorithm for flat F-manifolds associated with Landau-Ginzburg models

TL;DR

This paper introduces a perturbative algorithm to construct formal flat F-manifold structures on cohomologies related to Landau-Ginzburg models, enabling new insights into algebraic and geometric structures in mathematical physics.

Contribution

It presents a novel perturbative method for constructing flat F-manifold structures on cohomologies of dGBV algebras associated with Landau-Ginzburg models, applicable to Jacobian algebras and Calabi-Yau intersections.

Findings

Constructed flat F-manifold structures on Jacobian algebras.

Built flat F-manifold structures on primitive cohomology of Calabi-Yau intersections.

Provided a systematic perturbative approach for these geometric structures.

Abstract

We develop a perturbative algorithm for constructing formal flat $F$-manifold structures on the cohomologies of dGBV (differential Gerstenhaber-Batalin-Vilkovisky) algebras associated with Landau-Ginzburg models. As an application, this approach provides a perturbative construction of formal flat $F$-manifold structures on two important objects: the Jacobian algebra of a homogeneous polynomial with an isolated singularity at the origin, and the primitive cohomology of smooth projective Calabi-Yau complete intersections.