Quantization and 2π periodicity of the axion action in topological insulators

The Lagrangian describing the bulk electromagnetic response of a three-dimensional strong topological insulator contains a topological axion term of the form theta E.B. It is often stated (without proof) that the corresponding action is quantized on periodic space time and therefore invariant under theta >theta+2 pi. Here we provide a simple, physically motivated proof of the axion action quantization on the periodic space time, assuming only that the vector potential is consistent with single valuedness of the electron wave functions in the underlying insulator.