Tearing Fractons

TL;DR

This paper introduces a fractonic gauge theory duality to explain the constraints on folding and tearing in elastic sheets, revealing fundamental links between mechanical behavior and fracton physics.

Contribution

It establishes a duality between elastic plate theory and a fractonic gauge theory, providing a novel framework to understand folding and tearing constraints.

Findings

Fold defects correspond to vector charges in the gauge theory.

Fractonic constraints restrict fold movement to the growth direction.

Tearing corresponds to fracton motion perpendicular to the fold.

Abstract

We offer a fractonic perspective on a familiar observation -- a flat sheet of paper can be folded only along a straight line if one wants to avoid the creation of additional creases or tears. Our core underlying technical result is the establishment of a duality between the theory of elastic plates and a fractonic gauge theory with a second rank symmetric electric field tensor, a scalar magnetic field, a vector charge, and a symmetric tensor current. Bending moment and momentum of the plate are dual to the electric and magnetic fields, respectively. While the flexural waves correspond to the quadratically dispersing photon of the gauge theory, a fold defect is dual to its vector charge. Crucially, the fractonic condition constrains the latter to move only along its direction, i.e., the fold's growth direction. By contrast, fracton motion in the perpendicular direction amounts to tearing the paper.