The $\theta$-term is also known as the axion term and it's simply the $F\wedge F$ term known to particle physicists. In a more condensed-matter-friendly language,
$$\Delta {\mathcal L} = \theta\left( \frac{e^2}{2\pi h} \right) \vec B \cdot \vec E $$
I don't know the optimum starting point but you may begin with

http://arxiv.org/abs/1001.3179

and its followups and references. More generally, the $\theta$-term means the integral of the anomaly polynomial. Note that the anomaly polynomial is a nice gauge-invariant expression - but in higher dimensions. The actual anomaly in the original spacetime is related to it by several operations.

This post imported from StackExchange Physics at 2014-04-11 15:46 (UCT), posted by SE-user Luboš Motl