Partition Functions and Stability Criteria of Topological Insulators

The non-chiral edge excitations of quantum spin Hall systems and topological insulators are described by means of their partition function. The stability of topological phases protected by time-reversal symmetry is rediscussed in this context and put in relation with the existence of discrete anomalies and the lack of modular invariance of the partition function. The $\Z_2$ characterization of stable topological insulators is extended to systems with interacting and non-Abelian edge excitations.