Hamiltonian BRST deformation of a class of n-dimensional BF-type theories

TL;DR

This paper develops a Hamiltonian BRST deformation method to construct consistent interactions in higher-dimensional BF-type theories, revealing their relation to Poisson structures on the target space.

Contribution

It introduces a cohomological Hamiltonian BRST deformation approach for adding interactions to abelian BF theories in dimensions four and above, highlighting their connection to Poisson manifolds.

Findings

Constructed consistent Hamiltonian interactions for BF theories in n≥4 dimensions.

Revealed the relation between Hamiltonian couplings and Poisson structures.

Demonstrated the resulting models have open, on-shell reducible first-class constraint algebras.

Abstract

Consistent Hamiltonian interactions that can be added to an abelian free BF-type class of theories in any n greater or equal to 4 spacetime dimensions are constructed in the framework of the Hamiltonian BRST deformation based on cohomological techniques. The resulting model is an interacting field theory in higher dimensions with an open algebra of on-shell reducible first-class constraints. We argue that the Hamiltonian couplings are related to a natural structure of Poisson manifold on the target space.