  Spurred by recent development of fracton topological phases, unusual
topological phases possessing fractionalized quasi-particles with mobility
constraints, the concept of symmetries has been renewed. In particular, in
accordance with the progress of multipole symmetries, associated with
conservation of multipoles, such as dipole or quadruple moments as well as
global charges, there have been proposed topological phases with such
symmetries. These topological phases are unconventional as excitations are
subject to mobility constraints corresponding to the multipole symmetries. We
demonstrate a way to construct such phases by preparing layers of symmetry
protected topological (SPT) phases and implementing gauging a global symmetry.
After gauging, the statistics of a fractional excitation is altered when
crossing the SPT phases, resulting in topological phases with the multipole
symmetries. The way we construct the phases allows us to have a comprehensive
understanding of field theories of topological phases with the multipole
symmetries and other fracton models.
