  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
post-gauging 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.
