UV-IR mixing and the quantum consistency of noncommutative gauge theories

TL;DR

This paper investigates the quantum consistency of noncommutative gauge theories, revealing new UV-IR divergences that challenge their renormalizability and highlighting their sensitivity to ultraviolet behavior.

Contribution

It demonstrates the emergence of novel UV-IR divergences in noncommutative gauge theories and shows that renormalizability generally fails beyond one-loop in non-supersymmetric cases.

Findings

New UV-IR divergences found during Wilsonian analysis

Renormalizability fails in non-supersymmetric noncommutative gauge theories

Quantum corrections beyond one-loop compromise renormalizability

Abstract

We study the quantum mechanical consistency of noncommutative gauge theories by perturbatively analyzing the Wilsonian quantum effective action in the matrix formulation. In the process of integrating out UV states, we find new divergences having dual UV-IR interpretations and no analogues in ordinary quantum field theories. The appearance of these new UV-IR divergences has profound consequences for the renormalizability of the theory. In particular, renormalizability fails in any nonsupersymmetric noncommutative gauge theory. In fact, we argue that renormalizability generally fails in any noncommutative theory that allows quantum corrections beyond one-loop. Thus, it seems that noncommutative quantum theories are extremely sensitive to the UV, and only the softest UV behavior can be tolerated.