Dispersion relations for dislocation modes and their sensitivity to the lattice structure

In this work, we show that the dispersion relation for the dynamical modes of dislocations (``dislons'') in solids is sensitive to the lattice symmetries. In particular, we show that, in the IR, the dislon dispersion relation develops a logarithmic dependence on momenta for approximately isotropic lattices, whereas for nonisotropic lattices, the linear term dominates. The renormalization group flows for dislocation tension are shown to be distinct for isotropic and anisotropic lattices.