Infrared and Ultraviolet Finiteness of Topological BF Theory in Two Dimensions

TL;DR

This paper demonstrates that the two-dimensional topological BF theory remains finite at all orders in perturbation theory when an infrared regulator is introduced, highlighting its renormalizability and finiteness.

Contribution

It shows the perturbative finiteness of the 2D topological BF model by analyzing its supersymmetric algebraic structure with an infrared regulator.

Findings

The model is perturbatively finite.

Infrared regulator ensures well-behaved ghost propagator.

Supersymmetric algebraic structure underpins renormalizability.

Abstract

The two--dimensional topological BF model is considered in the Landau gauge in the framework of perturbation theory. Due to the singular behaviour of the ghost propagator at long distances, a mass term to the ghost fields is introduced as infrared regulator. Relying on the supersymmetric algebraic structure of the resulting massive theory, we study the infrared and ultraviolet renormalizability of the model, with the outcome that it is perturbatively finite.