Publication : t92/124

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 {\ninetit\char'016}-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 $0d^{\star}$ in the attractive case is thus established. To our knowledge, this study 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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