Interacting Crumpled Manifolds: Exact Results to all Orders of Perturbation Theory

Abstract

In this letter, we report progress on the field theory of polymerized tethered membranes. For the toy-model of a manifold repelled by a single point, we are able to sum the perturbation expansion in the strength g of the interaction exactly in the limit of internal dimension D -> 2. This exact solution is the starting point for an expansion in 2-D, which aims at connecting to the well studied case of polymers (D=1). We here give results to order (2-D)^4, where again all orders in g are resummed. This is a first step towards a more complete solution of the self-avoiding manifold problem, which might also prove valuable for polymers.