Field theoretic operators for multifractal moments

While multifractal spectra are convex, general field theoretic arguments show that power of field operators $\phi^f$ 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 $\phi,\psi$, operators $O_{f'f}=\psi^{f'}\phi^f$ with traceless symmetry give rise to multifractal spectra of harmonic diffusion near absorbing fractals when evaluated for zero component fields.