Are sponge phases of membranes experimental gauge-Higgs systems?

Abstract

A simple generalization of a continuum model of fluctuating membranes is considered in which one allows the existence of holes as structural defects. The proposed phase diagram of such systems includes, in particular, a variety of ‘‘sponge’’ phases now exhibiting edges in the form of closed loops or infinite lines. We show that the simplest theory describing the transitions between these phases is identical to the lattice gauge theory for a ${\mathit{Z}}_2$ Higgs system. We suggest, therefore, that sponge phases of amphiphilic films could form experimental models to check some of the nontrivial predictions of lattice gauge theories.