Interacting crumpled manifolds: Exact results to all orders of perturbation theory

¹ Fachbereich Physik, Universität Essen - 45117 Essen, Germany
² KITP, Kohn Hall, University of California at Santa Barbara Santa Barbara, CA 93106, USA

Corresponding authors: pinnow@theo-phys.uni-essen.de wiese@itp.ucsb.edu

Received: 1 October 2002
Accepted: 20 August 2003

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 g₀ of the interaction exactly in the limit of internal dimension . This exact solution is the starting point for an expansion in , which aims at connecting to the well-studied case of polymers (). We here give results to order , where again all orders in g₀ 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.