Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1)

Abstract

U(1) gauge theory on non-commutative Minkowski space-time in the Feynman-'t Hooft background gauge is studied. In particular, UV divergences and non-commutative IR divergent contributions to the two, three and four-point functions are explicitly computed at one loop. We show that the negative sign of the beta function results from paramagnetism --producing UV charge anti-screening-- prevailing over diamagnetism --giving rise toUV charge screening. This dominance in the field theory setting corresponds to tachyon magnification dominance in the string theory framework. Our calculations provide an explicit realization of UV/IR mixing and lead to an IR renormalization of the coupling constant, where now paramagnetic contributions produce screening and diamagnetic contributions anti-screening.

39 pages, 7 eps figures; typos corrected, few comments added

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• Noncommutative Perturbative Dynamics
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• Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
• Excitations in Hot Non-Commutative Theories
• A Note On Space Noncommutativity
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