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Renormalization of crumpled manifolds

Abstract : 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.
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Contributor : Bruno Savelli <>
Submitted on : Tuesday, February 5, 2019 - 3:14:11 PM
Last modification on : Wednesday, April 14, 2021 - 12:12:27 PM

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



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