Noncommutative Two Dimensional BF Model

TL;DR

This paper investigates the noncommutative extension of the 2D BF theory, revealing that noncommutativity introduces infinitely many quantum corrections, challenging standard quantum field theory rules and raising concerns about noncommutative anomalies.

Contribution

It demonstrates that noncommutative deformation of 2D BF theory leads to infinitely many quantum terms, highlighting fundamental issues in noncommutative quantum field theories.

Findings

Noncommutative parameter induces infinite quantum corrections.

Challenges standard QFT rules in noncommutative settings.

Detailed analysis of noncommutative anomalies provided.

Abstract

We consider the noncommutative extension of the BF theory in two spacetime dimensions. We show that the introduction of the noncommutative parameter \theta_{\mu\nu}, already at first order in the analytical sector, induces infinitely many terms in the quantum extension of the model. This clashes with the commonly accepted rules of QFT, and we believe that this problem is not peculiar to this particular model, but it might concern the noncommutative extension of any ordinary quantum field theory obtained via the Moyal prescription. A detailed study of noncommutative anomalies is also presented.