Anomalies of non-invertible self-duality symmetries: fractionalization and gauging

Understand

We study anomalies of non-invertible duality symmetries in both 2d and 4d, employing the tool of the Symmetry TFT.

• In the 2d case we rephrase the known obstruction theory for the Tambara-Yamagami fusion category in a way easily generalizable to higher dimensions.
• In both cases we find two obstructions to gauging duality defects.
• The first obstruction requires the existence of a duality-invariant Lagrangian algebra in a certain Dijkgraaf-Witten theory in one dimension more.