Renormalization of Crumpled Manifolds
F. David, B. Duplantier, E. Guitter
Abstract
We consider a model of D-dimensional tethered manifold interacting by excluded volume in Rd with a single point. By use of intrinsic distance geometry, we first provide a rigorous definition of the analytic continuation of its perturbative expansion for arbitrary D, 0 < D < 2. We then construct explicitly a renormalization operation, ensuring renormalizability to all orders. This is the first example of mathematical construction and renormalization for an interacting extended object with continuous internal dimension, encompassing field theory.
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