Extention cohomological fields theories and noncommutative Frobenius manifolds

TL;DR

This paper develops an extension of Cohomological Field Theory called Stable Field Theory, which uses tensor series satisfying differential equations to produce noncommutative Frobenius algebra analogues for open-closed topological field theories.

Contribution

It introduces Stable Field Theory as a new framework extending Cohomological Field Theory with noncommutative Frobenius structures.

Findings

Constructed Stable Field Theory system of homomorphisms

Derived noncommutative Frobenius algebra analogues

Linked tensor series solutions to open-closed topological field theories

Abstract

We construct some extension ({\it Stable Field Theory}) of Cohomological Field Theory. The Stable Field Theory is a system of homomorphisms to some vector spaces generated by spheres and disks with punctures. It is described by a formal tensor series, satisfying to some system of "differential equations". In points of convergence the tensor series generate special noncommutative analogues of Frobenius algebras, describing 'Open-Closed' Topological Field Theories.