Climbing the ladder of topological bosonic orbifold phases in the orthogonal family: from gauging dihedral symmetry to metaplectic anyons and more

We present a coupled-wire model of a family of bosonic orbifold topological phases in two spatial dimensions using strongly interacting electrons with a charge 4e superconducting pairing. A topological phase M can carry a global discrete symmetry G. We focus on the bosonic SO(2n)₁ family that exhibits a dihedral D_k symmetry. The symmetry may become local when the system undergoes a phase transition that allows gauge fluxes and charges to emerge. These new phases M / G, referred to as twist liquids, host boundary edge modes that can be effectively described by an orbifold conformal field theory. We explicitly demonstrate these in the bosonic orbifold series of U(1)_l / Z₂, SO(2n)₁ / Z_k, SU(n)₁ / Z₂ and SO(2n)₁ / D_k, and present their quasiparticle excitations.