Renormalization Theory for Interacting Crumpled Manifolds

Details Renormalization Theory for Interacting Crumpled Manifolds Renormalization Theory for Interacting Crumpled Manifolds

1992-11-09

arxiv.org/abs/hep-th/9211038v1

Nucl.Phys. B394 (1993) 555-664

Physics

High Energy Physics

High Energy Physics - Theory

126 pages (+ 24 figures not included available upon request), harvmac, SPhT/92/124

Scientific paper

10.1016/0550-3213(93)90226-F

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 0d* 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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