The finiteness of the four dimensional antisymmetric tensor field model in a curved background

TL;DR

This paper constructs a renormalizable supersymmetric model for a four-dimensional antisymmetric tensor field in curved space-time, proving its ultraviolet finiteness to all orders using algebraic methods.

Contribution

It introduces a rigid supersymmetry framework for the tensor field model in curved backgrounds and demonstrates its all-order ultraviolet finiteness.

Findings

Supersymmetry algebra closes only with a covariantly constant vector parameter.

The model is proven to be ultraviolet finite to all perturbative orders.

The algebraic proof ensures the model's consistency and finiteness in curved space.

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.