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arXiv · hep-th/9211038

Renormalization Theory for Interacting Crumpled Manifolds

F. David·B. Duplantier·E. Guitter
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Abstract

We consider a continuous model of D-dimensional elastic (polymerized) manifold fluctuating in d-dimensional Euclidean space, interacting with a single impurity via an attractive or repulsive delta-potential (but without self-avoidance interactions). Except for D=1 (the polymer case), this model cannot be mapped onto a local field theory. We show that the use of intrinsic distance geometry allows for a rigorous construction of the high-temperature perturbative expansion and for analytic continuation in the manifold dimension D. We study the renormalization properties of the model for 0 d* in the attractive case is thus established. To our knowledge, this provides the first proof of renormalizability for a model of extended objects, and should be applicable to the study of self-avoidance interactions for random manifolds.

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F. David, B. Duplantier, E. Guitter. 1992-11-09. Renormalization Theory for Interacting Crumpled Manifolds. https://doi.org/10.1016/0550-3213(93)90226-f

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