Chapline–manton Interaction Vertices and Hamiltonian BRST Cohomology

Abstract

Consistent interactions between Yang-Mills gauge fields and an abelian 2-form are investigated by using a Hamiltonian cohomological procedure. It is shown that the deformation of the BRST charge and the BRST-invariant Hamiltonian of the uncoupled model generates the Yang-Mills Chern-Simons interaction term. The resulting interactions deform both the gauge transformations and their algebra, but not the reducibility relations.

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

“…It has been shown in [6] that the problem of constructing consistent Hamiltonian interactions in theories with first-class constraints can be equivalently reformulated as a deformation problem of the BRST charge Ω 0 and of the BRST-invariant Hamiltonian H 0B of a given "free" first-class theory. More precisely, if the interactions can be consistently constructed, then the "free" BRST charge can be deformed into…”

“…In a similar manner, we deform the BRST-invariant Hamiltonian of the "free" theory 6) and require that it stands for the BRST-invariant Hamiltonian of the coupled system…”

“…3) 5) and displaying the first-class Hamiltonian 6) in terms of the non-vanishing fundamental Dirac brackets…”

“…The equation (4.1) projected on antighost number (J − 1) becomes 6) and it shows that a necessary condition for the existence of (J−1) ω 1 is that the functions a J from (4.5) belong to H J δ|d , where the last notation means the homological space of the Koszul-Tate differential modulo the spatial part of the exterior spacetime derivative at antighost number J. Equivalently, these functions should satisfy the equation…”

“…The understanding of this symmetry on cohomological grounds made possible a unitary approach to many problems in gauge field theory, such as the Hamiltonian analysis of anomalies [4], the precise relation between local Lagrangian and Hamiltonian BRST cohomologies [5], and, recently, the problem of obtaining consistent Hamiltonian interactions in gauge theories by means of the deformation theory [6,7,8].…”