Renormalization Theory for Interacting Crumpled Manifolds
| dc.creator | David, F. | |
| dc.creator | Duplantier, B. | |
| dc.creator | Guitter, E. | |
| dc.date | 1992-11-09 | |
| dc.date.accessioned | 2026-07-07T07:44:43Z | |
| dc.date.available | 2026-07-07T07:44:43Z | |
| dc.description | 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<2, and show that for d<d* where d*=2D/(2-D) is the upper critical dimension, the perturbative expansion is UV finite, while UV divergences occur as poles at d=d*. The standard proof of perturbative renormalizability for local field theories (the BPH theorem) does not apply to this model. We prove perturbative renormalizability to all orders by constructing a subtraction operator based on a generalization of the Zimmermann forests formalism, and which makes the theory finite at d=d*. This subtraction operation corresponds to a renormalization of the coupling constant of the model (strength of the interaction with the impurity). The existence of a Wilson function, of an epsilon-expansion around the critical dimension, of scaling laws for d<d* in the repulsive case, and of non-trivial critical exponents of the delocalization transition for d>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. | |
| dc.description | 126 pages (+ 24 figures not included available upon request), harvmac, SPhT/92/124 | |
| dc.identifier | https://arxiv.org/abs/hep-th/9211038 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9211038 | |
| dc.identifier | Nucl.Phys. B394 (1993) 555-664 | |
| dc.identifier | doi:10.1016/0550-3213(93)90226-F | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123296 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Condensed Matter | |
| dc.title | Renormalization Theory for Interacting Crumpled Manifolds | |
| dc.type | text |