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

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.

RevTex, 13 pages, 9 figures, To be published in PRD

References in corpus (1)

• On the UV renormalizability of noncommutative field theories

Cited by in corpus (6)

• Renormalizability of noncommutative SU(N) gauge theory
• The one-loop renormalization of the gauge sector in the noncommutative standard model
• Superfield covariant analysis of the divergence structure of noncommutative supersymmetric QED${}_4$
• On the finiteness of noncommutative supersymmetric QED${}_3$ in the covariant superfield formulation
• BRST Quantization of Noncommutative Gauge Theories
• Softer Hard Scattering and Noncommutative Gauge-String Duality