论文标题
撕裂的分裂
Tearing Fractons
论文作者
论文摘要
我们在熟悉的观察结果上提供了分数的观点 - 如果要避免产生额外的折痕或眼泪，只有直线折叠的平坦纸才能折叠。我们的核心潜在技术结果是弹性板理论与具有第二等级对称电场张量，标量磁场，向量电荷和对称张量电流的分形量规理论之间建立了双重性。板的弯矩和动量分别对电场和磁场是双重的。虽然弯曲波对应于量规理论的四次分散光子，但折叠缺陷是其矢量电荷双重的。至关重要的是，分形条件限制了后者仅沿其方向移动，即折叠的生长方向。相比之下，垂直方向的分裂运动等于撕裂纸张。
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.
