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arXiv · 2510.10773

The Freed--Quinn line bundle from higher geometry

Daniel Berwick-Evans·Emily Cliff·Laura Murray
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Abstract

For a finite group $G$, and level $\alpha\in Z^3(BG;{\rm U}(1))$, 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.

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Daniel Berwick-Evans, Emily Cliff, Laura Murray. 2025-10-12. The Freed--Quinn line bundle from higher geometry. https://arxiv.org/abs/2510.10773

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