Motrunich, Olexei2015-05-212015-05-212015-05https://hdl.handle.net/11299/172317Motivated by ideas of fractionalization and topological order in bosonic models with short-range interactions, we consider similar phenomena in formal lattice gauge theory models, which are models where basic constituents are quantum lines. In the first example, we show that a compact quantum electrodynamics (CQED) can have, besides familiar Coulomb and confined phases, additional unusual confined phases where excitations are quantum lines carrying fractions of the elementary unit of electric field strength; specifically, we construct a model that has $N$-tupled monopole condensation and realizes 1/N fractionalization of the quantum Faraday lines. In the second example, we consider a system consisting of two copies of CQED in (4+1)D and engineer condensation of bound states of monopoles (which are quantum lines in four spatial dimensions) and U(1) electric field lines. When the bound states contain a single monopole, we find lattice gauge theory analogs of Symmetry Protected Topological phases, while when the bound states contain multiple monopoles, we find analogs of Symmetry-Enriched Topological phases, where we also have fractionalization of Faraday lines. The distinct character of these “topological” phases of quantum lines is revealed by unusual response properties and physics at a boundary of a spatial region in such a phase.enFTPISymmetriesPresentation