Fractonic line excitations : an inroad from 3d elasticity theory
Shriya Pai, Michael Pretko
TL;DR
The paper develops a three-dimensional fracton–elasticity duality by mapping 3D crystal elasticity onto a rank-4 tensor gauge theory. In this framework, disclination lines become fractonic line charges with conserved surface flux, while dislocations correspond to flux dipoles, yielding mobility restrictions governed by generalized higher-moment conservation laws. The authors derive the relevant Gauss's law, gauge transformations, and continuum equations, and they analyze the energetics of line defects, showing distinct scaling for disclinations and dislocations. They also explore generalizations to other tensor gauge theories, highlighting potential applications to 3D melting and robust quantum error-correcting codes.
Abstract
We demonstrate the existence of a fundamentally new type of excitation, fractonic lines, which are line-like excitations with the restricted mobility properties of fractons. These excitations, described using an amalgamation of higher-form gauge theories with symmetric tensor gauge theories, see direct physical realization as the topological lattice defects of ordinary three-dimensional quantum crystals. Starting with the more familiar elasticity theory, we show how it maps onto a rank-4 tensor gauge theory, with phonons corresponding to gapless gauge modes and disclination defects corresponding to line-like charges. We derive flux conservation laws which lock these line-like excitations in place, analogous to the higher moment charge conservation laws of fracton theories. This way of encoding mobility restrictions of lattice defects could shed light on melting transitions in three dimensions. This new type of extended object may also be a useful tool in the search for improved quantum error-correcting codes in three dimensions.