The Finiteness of the Four-Dimensional Antisymmetric Tensor Field Model in a Curved Background

Abstract

A renormalizable rigid supersymmetry for the four-dimensional antisymmetric tensor field model in a curved space-time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the vector parameter of the supersymmetry is a covariantly constant vector field. This also guarantees that the corresponding transformations lead to a genuine symmetry of the model. The proof of the ultraviolet finiteness to all orders of perturbation theory is performed in a pure algebraic manner by using the rigid supersymmetry.

Ultraviolet and Infrared Finiteness in Two Dimensional Curved Space-Time

“…As for the other topological gauge field models [13], [24], [7], [26], the metric g µν is only present in the gauge fixing part of the action which is nothing else but an exact BRS variation. This fact implies that, here, one can also extend the BRS symmetry [19] by letting the operator s acting on the background metric as:…”