Rigid Chiral Membranes

TL;DR

This paper investigates the effects of a unique chiral coupling in flexible membranes, showing how thermal fluctuations influence its behavior and implications for lipid bilayers with tilted chiral molecules.

Contribution

It identifies a single parity-breaking coupling in membrane models and analyzes its renormalization-group flow under thermal fluctuations.

Findings

The coupling is the only allowed parity-breaking term in such membranes.

Thermal fluctuations diminish the coupling at large scales.

Implications for chiral lipid bilayer behavior.

Abstract

Statistical ensembles of flexible two-dimensional fluid membranes arise naturally in the description of many physical systems. Typically one encounters such systems in a regime of low tension but high stiffness against bending, which is just the opposite of the regime described by the Polyakov string. We study a class of couplings between membrane shape and in-plane order which break 3-space parity invariance. Remarkably there is only {\it one} such allowed coupling (up to boundary terms); this term will be present for any lipid bilayer composed of tilted chiral molecules. We calculate the renormalization-group behavior of this relevant coupling in a simplified model and show how thermal fluctuations effectively reduce it in the infrared.