Fluid Membranes and 2d Quantum Gravity

TL;DR

This paper investigates the renormalization group flow of two-dimensional fluid membranes using functional RG methods, exploring fixed points and proposing a connection to two-dimensional quantum gravity.

Contribution

It introduces a truncation ansatz including curvature terms to derive beta functions and suggests a novel link between membrane theory and quantum gravity in the zero-dimensional limit.

Findings

No evidence for a crumpling transition at non-zero temperature.

Derived beta functions for surface tension, bending, and Gaussian rigidity.

Proposed the D→0 limit as a model for two-dimensional quantum gravity.

Abstract

We study the 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, bending rigidity and Gaussian rigidity. We look for non-trivial fixed points but we find no evidence for a crumpling transition at $T\neq0$. Finally, we propose to identify the $D\rightarrow 0$ limit of the theory with two dimensional quantum gravity. In this limit we derive new beta functions for both cosmological and Newton's constants.