Mathematical Structures of Cohomological Field Theories
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Submission date: 08. Mar. 2022
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A mathematical definition of Cohomological Lagrangian Field Theories (CoLFTs) is formulated in the language of graded/bi-graded manifolds. Algebraic properties of observables in CoLFTs are studied. Methods of constructing CoLFTs, 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.