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 spacetime 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 to UV 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 LR renormalization of the coupling constant, where now paramagnetic contributions produce screening and diamagnetic contributions anti-screening.