Regularized bosonic strings need extrinsic curvature |
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| Affiliation: | 1. Department of Molecular Physiology and Biophysics, University of Iowa College of Medicine, Iowa City, IA 52246, USA;2. Theoretical and Computational Biophysics Group, NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA;3. Department of Biochemistry, and Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA;4. Unnatural Protein Facility, Department of Biochemistry and Biophysics, Oregon State University, Corvallis, OR 97331, USA;5. Laboratoire International Associé CNRS-University of Illinois, Unité mixte de recherche n°70a9, Université de Lorraine, France;6. Department of Physics, University of Illinois at Urbana−Champaign, Urbana, IL 61801, USA |
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| Abstract: | We show that the string tension in a class of triangulated random surface models with gaussian action does not tend to zero at the critical point. This rules out the existence of a non-trivial continuum limit of these models. Furthermore, the proof seems to lead to the conclusion that the most natural (if not the only) way to avoid this feature of random surface models is by introducing asymptotically free interactions depending e.g. on the extrinsic curvature of the surface. |
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