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• W3105322471 abstract "We show that renormalized non-commutative scalar field theories do not reduce to their planar sector in the limit of large non-commutativity. This follows from the fact that the RG equation of the Wilson-Polchinski type which describes the genus zero sector of non-commutative field theories couples generic planar amplitudes with non-planar amplitudes at exceptional values of the external momenta. We prove that the renormalization problem can be consistently restricted to this set of amplitudes. In the resulting renormalized theory non-planar divergences are treated as UV divergences requiring appropriate non-local counterterms. In 4 dimensions the model turns out to have one more relevant (non-planar) coupling than its commutative counterpart. This non-planar coupling is ``evanescent'': although in the massive (but not in the massless) case its contribution to planar amplitudes vanishes when the floating cut-off equals the renormalization scale, this coupling is needed to make the Wilsonian effective action UV finite at all values of the floating cut-off." @default.
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• W3105322471 date "2003-08-01" @default.
• W3105322471 modified "2023-09-24" @default.
• W3105322471 title "The renormalization of non-commutative field theories in the limit of large non-commutativity" @default.
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• W3105322471 doi "https://doi.org/10.1016/s0550-3213(03)00436-x" @default.
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