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Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of the two. Here we develop a gauging procedure for general submanifold symmetries of Pauli Hamiltonians, including symmetries of fractal type. We show a relation between the pre- and postgauging models and use this to construct short-range entangled phases with fractal-like symmetries, one of which is mapped to the cubic code by the gauging.
Dominic J. Williamson (Mon,) studied this question.