Minimal Fractal Manifold as Asymptotic Regime of Non-Commutative Field Theory

Abstract

The minimal fractal manifold (MFM) defines a space-time continuum endowed with arbitrarily small deviations from four-dimensions (e = 4 – D, e  << ). It was recently shown that MFM is a natural consequence of the Renormalization Group and that it brings up a series of unforeseen solutions to the challenges raised by the Standard Model. In this brief report we argue that MFM may be treated as asymptotic manifestation of Non-Commutative (NC) Field Theory near the electroweak scale. Our provisional findings may be further expanded to bridge the gap between MFM and NC Field Theory.