Multifractals and Lagrangian field theory

We discuss some general aspects of ‘multifractal scaling’ in the context of continuum Lagrangian field theories and, in particular, an observation of Duplantier and Ludwig that sequences of scaling variables which couple additively in their operator product expansion (OPE) exhibit multifractal scaling of their integer moments. We show that, for positive variables, multifractal scaling of the integer moments implies, along subsequences, multifractal scaling of all continuous moments and, automatically, ‘subadditivity’ of the scaling exponent in the moment index. A perturbative criterion of positivity is suggested. Finally, some prospects for additively-coupled sequences and multifractal scaling in stable Lagrangian field theories are considered.