Fluid membranes and 2d quantum gravity

We study the renormalization-group (RG) flow of two dimensional (fluid) membranes embedded in Euclidean D-dimensional space using functional RG methods based on the effective average action. By considering a truncation ansatz for the effective average action with both extrinsic and intrinsic curvature terms, we derive a system of beta functions for the running surface tension μk, bending rigidity κk, and Gaussian rigidity κ̄k. We look for nontrivial fixed points but we find no evidence for a crumpling transition at T0. Finally, we propose to identify the D→0 limit of the theory with two dimensional quantum gravity. In this limit, we derive new beta functions for both cosmological and Newton's constants. © 2011 American Physical Society.