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Keywords:
Quantum field theory; anomalies; factorization algebras; $\Bbb E_n$-algebras; Gelfand–Fuchs cohomology; Poisson structures; supergravity
Quantum field theory; anomalies; factorization algebras; $\Bbb E_n$-algebras; Gelfand–Fuchs cohomology; Poisson structures; supergravity
Summary:
We construct a class of quantum field theories depending on the data of a holomorphic Poisson structure on a piece of the underlying spacetime. The main technical tool relies on a characterization of deformations and anomalies of such theories in terms of the Gelfand--Fuchs cohomology of formal Hamitlonian vector fields. In the case that the Poisson structure is non-degenerate such theories are topological in a certain weak sense, which we refer to as “de Rham topological”. While the Lie algebra of translations acts in a homotopically trivial way, we will show that the space of observables of such a theory does not define an $\Bbb E_n$-algebra. Additionally, we will highlight a conjectural relationship to theories of supergravity in four and five dimensions.
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