Holomorphic Poisson Field Theories

Abstract

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.

On the associativity of 1-loop corrections to the celestial operator product in gravity

“…Here we briefly review the elements needed for this paper, which are fairly minimal. For a more extensive description of the BV formulation of holomorphic theories we refer the reader to [48], and for the particular case of Poisson-BF theory to [49].…”

Snowmass White Paper: The Quest to Define QFT

“…Therefore, the likely status of the FA approach is that it provides an alternative viewpoint, and technically quite a different approach to constructing concrete models. Some papers that use this framework include [473][474][475][476][477][478][479][480][481][482][483][484][485][486][487][488], also [489][490][491][492]. It is also suggested by [493] that this approach has close relations to [494].…”