Renormalization and hyperscaling for self-avoiding manifold models

Abstract : The renormalizability of the self-avoiding manifold Edwards model is established. We use a new short distance multilocal operator product expansion, which extends methods of local field theories to a large class of models with nonlocal singular interactions. This validates the direct renormalization method introduced before, as well as scaling laws. A new general hyperscaling relation is derived. Manifolds at the $\Theta$ point and long-range Coulomb interactions are briefly discussed.