Derivative Expansion of One-Loop Effective Energy of Stiff Membranes with Tension

TL;DR

This paper develops a derivative expansion method to calculate one-loop thermal fluctuation corrections to the energy of nearly flat, stiff membranes with tension, revealing renormalizability and divergence cancellations.

Contribution

It introduces a novel derivative expansion approach allowing arbitrary tilt in membrane energy calculations, ensuring renormalizability and analyzing divergence behaviors.

Findings

Ultraviolet divergences match the original energy form.

Infrared divergences cancel nontrivially.

Method accommodates arbitrary membrane tilt.

Abstract

With help of a derivative expansion, the one-loop corrections to the energy functional of a nearly flat, stiff membrane with tension due to thermal fluctuations are calculated in the Monge parametrization. Contrary to previous studies, an arbitrary tilt of the surface is allowed to exhibit the nontrivial relations between the different, highly nonlinear terms accompanying the ultraviolet divergences. These terms are shown to have precisely the same form as those in the original energy functional, as necessary for renormalizability. Also infrared divergences arise. These, however, are shown to cancel in a nontrivial way.