Gauge Dynamics and Topological Insulators

A non-abelian magnetic field in Yang-Mills theory induces the formation of a "W-boson" vortex lattice. We study the propagation of fundamental fermions in the presence of this lattice in 2+1 dimensions. We show that the spectrum for massless fermions contains four topologically-protected Dirac points with non-zero Bloch momentum. For massive fermions, we compute topological invariants of the band structure and show that it is possible to realise a Z2 topological insulator within Yang-Mills theory.