Mapping Effective Field Theory to Multifractal Geometry

Fractals and multifractals are well-known trademarks of nonlinear dynamics and classical chaos. The goal of this work is to tentatively uncover the unforeseen path from multifractals and selfsimilarity to the framework of effective field theory (EFT). An intriguing finding is that the partition function of multifractal geometry includes the signature of non-Euclidean metric. Our results also suggest that multifractal geometry may offer insights into the non-renormalizable interactions presumed to develop beyond the Standard Model scale.