  Whereas electromagnetic surface waves are confined to a planar interface
between two media, line waves exist at the one-dimensional interface between
three materials. Here we derive a non-local integral equation for computing the
properties of line waves, valid for surfaces characterised in terms of a
general tensorial impedance. We find a good approximation -- in many cases --
is to approximate this as a local differential equation, where line waves are
one-dimensional analogues of surface plasmons bound to a spatially dispersive
metal. For anisotropic surfaces we find the oscillating decay of recently
discovered `ghost' line waves can be explained in terms of an effective gauge
field induced by the surface anisotropy. These findings are validated using
finite element simulations.
