Authors: Ervin Goldfain
We show that the flow from the ultraviolet to the infrared sector of any high-dimensional nonlinear field theory approaches chaotic dynamics in a universal way. This result stems from several independent routes to aperiodic behavior and implies that the infrared attractor of effective field theories is likely to replicate the geometry of multifractal sets. It is found that the Standard Model (SM) Lagrangian is characterized by a dominant generalized dimension D = 2, while the same dimension of the Einstein-Hilbert Lagrangian turns out to be D = 4 . On the one hand, this finding disfavors any field-theoretic unification of SM and General Relativity (GR). On the other, it hints that the continuous spectrum of dimensions lying between and may naturally account for the existence of non-baryonic Dark Matter.
Comments: 13 Pages. Under construction.
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