Cohomological Lagrangian field theory

TL;DR

This paper develops a geometric framework for classical cohomological field theories using advanced algebraic structures, and extends it with BV-BFV formalism, exemplified by Donaldson-Witten theory.

Contribution

It introduces a novel geometric approach for cohomological field theories and extends it with BV-BFV formalism, including a detailed example with Donaldson-Witten theory.

Findings

Framework based on $G^{igstar}$-algebras and gauge natural theories

BV-BFV extension incorporating cotangent lift of Donaldson-Witten theory

Provides a unified geometric perspective for cohomological field theories

Abstract

This paper introduces a geometric framework for classical cohomological field theories based on $G^{\star}$-algebras and gauge natural field theories. A BV-BFV extension of the framework is provided, which incorporates the cotangent lift of the Donaldson-Witten theory as an illustrative example.