Generalized 2D BF Model quantized in the axial gauge

TL;DR

This paper proves that the two-dimensional BF model coupled with topological matter, when quantized in the axial gauge, is ultraviolet finite and free of anomalies, leveraging its supersymmetry structure.

Contribution

It demonstrates the ultraviolet finiteness and anomaly freedom of the 2D BF model with matter in the axial gauge, using algebraic renormalization techniques.

Findings

Model is ultraviolet finite to all orders.

Model is free of anomalies.

Supersymmetry aids in renormalization analysis.

Abstract

We discuss the ultraviolet finiteness of the two-dimensional BF model coupled to topological matter quantized in the axial gauge. This noncovariant gauge fixing avoids the infrared problem in the two-dimensional space-time. The BF model together with the matter coupling is obtained by dimensional reduction of the ordinary three-dimensional BF model. This procedure furnishes the usual linear vector supersymmetry and an additional scalar supersymmetry. The whole symmetry content of the model allows to apply the standard algebraic renormalization procedure which we use to prove that this model is ultraviolet finite and anomaly free to all orders of perturbation theory.