MULTIFRACTALS AND LAGRANGIAN FIELD-THEORY

We discuss some general aspects of 'multifractal scaling' in the conte xt of continuum Lagrangian field theories and, in particular, an obser vation of Duplantier and Ludwig that sequences of scaling variables wh ich couple additively in their operator product expansion (OPE) exhibi t multifractal scaling of their integer moments. We show that, for pos itive 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 scali ng in stable Lagrangian field theories are considered.