Field theoretic operators for multifractal moments

Abstract

While multifractal spectra are convex, general field theoretic arguments show that power of field operators $ϕ^f$ yield a concave spectrum of exponents as function of $f$. This is resolved by appropriate choice of operators to describe multifractal moments. In a Lagrangian field theory of two mutually interacting species of fields $ϕ,ψ$, operators $O_{f'f}=ψ^{f'}ϕ^f$ with traceless symmetry give rise to multifractal spectra of harmonic diffusion near absorbing fractals when evaluated for zero component fields.