Mathematical structures of cohomological field theories

A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing CohFTs, with or without gauge symmetries, are discussed. In particular, a generalization of the Mathai-Quillen formalism is given. Examples such as topological quantum mechanics, topological sigma model, topological M-theory, and topological Yang-Mills theory can be obtained uniformly using this new formalism. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

A mathematical framework for cohomological field theories (CohFTs) is presented in the language of bigraded manifolds. The algebraic properties of operators in CohFTs are studied, and methods for constructing CohFTs with or without gauge symmetries are discussed. The Mathai-Quillen formalism is generalized, and this new formalism allows for a unified approach to obtaining examples such as topological quantum mechanics, topological sigma model, topological M-theory, and topological Yang-Mills theory.