2020/08/05 by Christopher T. Elliott, Elliott, Chris, Williams, Brian R
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2008.02302
openalex publication_date 2020/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 Hamiltonian 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 En-algebra. Additionally, we will highlight a conjectural relationship to theories of supergravity in four and five dimensions.