On Gauging Finite Symmetries by Higher Gauging Condensation Defects

Based on the work by C{\'o}rdova-Costa-Hsin (arXiv:2412.16681), we propose an EFT-style, Lagrangian procedure to gauge finite 0-form symmetries in untwisted Dijkgraaf-Witten gauge theories on closed oriented manifolds using higher gauging condensation defects and point out its limitations. Using this proposal, we construct effective actions of untwisted Dijkgraaf-Witten theories with Heisenberg gauge group over $\mathbb{Z}_p$ and show that the braiding data from Hopf link and the fusion rules match with the expected discrete gauge theories. We also study the symTFT implications of these effective Lagrangians and clarify their relations with higher group global symmetries.