# On the ultraviolet finiteness of parity-preserving $U(1) \times U(1)$ massive QED$_3$

## TL;DR

This paper proves that parity-preserving $U(1) imes U(1)$ massive QED$_3$ is ultraviolet finite and free of anomalies at all orders, using algebraic renormalization and the quantum action principle.

## Contribution

It provides a regularization-independent proof of the all-order ultraviolet finiteness and anomaly freedom of the model.

## Key findings

- Vanishing beta functions for gauge couplings and Chern-Simons mass
- All anomalous dimensions are zero
- Model is free of gauge and parity anomalies at all orders

## Abstract

The parity-preserving $U_A(1)\times U_a(1)$ massive QED$_3$ is ultraviolet finiteness -- exhibits vanishing $\beta$-functions, associated to the gauge coupling constants (electric and pseudochiral charges) and the Chern-Simons mass parameter, and all the anomalous dimensions of the fields -- as well as is parity and gauge anomaly free at all orders in perturbation theory. The proof is independent of any regularization scheme and it is based on the quantum action principle in combination with general theorems of perturbative quantum field theory by adopting the Becchi-Rouet-Stora (BRS) algebraic renormalization method in the framework of Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) subtraction scheme.