  Fractons are particles with restricted mobility. We give a symmetry-based
derivation of effective field theories of gapless phases with fractonic
topological defects, such as solids and supersolids, using a coset
construction. The resulting theory is identified as the Cosserat elasticity
theory, which reproduces the conventional symmetric elasticity theory at low
energies. The construction can be viewed as a dynamical realization of the
inverse Higgs mechanism. We incorporate topological defects such as
dislocations and disclinations, which are nontrivially related by the Bianchi
identities of defect gauge fields. The origin of the fractonic nature of
defects in those systems can be traced back to the semidirect product structure
of translational and rotational groups. The construction is immediately
extendable to higher dimensions and systems with broken translational
symmetries, such as solids, supersolids, and vortex crystals. We identify
Wess-Zumino terms in supersolids, which induce quasiparticle scatterings on
topological defects.
