Rigid Surfaces in a Space with Large Dimensionality

A field-theoretic model describing a two-dimensional rigid membrane embedded in a d -dimensional space is solved in the limit d → ∞ . Features suggested by renormalization group calculations are confirmed (decrease of the effective rigidity at large distance and appearance of a persistence length). However, the background around which these calculations are performed is shown to be unstable under fluctuations of the shape of the membrane of any wave number at large d .