Renormalization of crumpled manifolds

François David (1) , Bertrand Duplantier (1) , Emmanuel Guitter (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We consider a model of a $D$-dimensional tethered manifold interacting by excluded volume in $\mathbb{R}^d$ 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 R, 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.

Domains: Physics [physics]

François David, Bertrand Duplantier, Emmanuel Guitter. Renormalization of crumpled manifolds. Physical Review Letters, 1993, 70 (15), pp.2205-2208. ⟨10.1103/PhysRevLett.70.2205⟩. ⟨cea-02008069⟩