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We demonstrate the existence of a fundamentally new type of excitation,fractonic lines, which are line-like excitations with the restricted mobilityproperties of fractons. These excitations, described using an amalgamation ofhigher-form gauge theories with symmetric tensor gauge theories, see directphysical realization as the topological lattice defects of ordinarythree-dimensional quantum crystals. Starting with the more familiar elasticitytheory, we show how it maps onto a rank-4 tensor gauge theory, with phononscorresponding to gapless gauge modes and disclination defects corresponding toline-like charges. We derive flux conservation laws which lock these line-likeexcitations in place, analogous to the higher moment charge conservation lawsof fracton theories. This way of encoding mobility restrictions of latticedefects could shed light on melting transitions in three dimensions. This newtype of extended object may also be a useful tool in the search for improvedquantum error-correcting codes in three dimensions.

Fractonic line excitations : an inroad from 3d elasticity theory