The Freed--Quinn line bundle from higher geometry

For a finite group $G$, and level $\alpha \in Z^3(BG;\mathrm{U}(1))$, Freed and Quinn construct a line bundle over the moduli space of $G$-bundles on surfaces. Global sections determine the values of Chern–Simons theory at level $\alpha$ on surfaces. In this paper, we provide an alternate construction using tools from higher geometry: the pair $(G,\alpha )$ determines a 2-group group, and the Freed–Quinn line arises as a categorical truncation of the bicategory of 2-group bundles.