Lattice Edge Theories for Topological Phases of Matter

Edge excitations of (2+1)D topological phases are usually described using continuum field theories. But the boundaries of some (2+1)D topological phases can also be described using lattice-like edge theories that have a finite dimensional Hilbert space for a finite size boundary. I will discuss several examples of such finite dimensional edge theories. The most interesting examples are ``ungappable'': they have the property that they cannot be gapped by any local interaction.