Gauging U(1) symmetry in (2+1)d topological phases

We study the gauging of a global U(1) symmetry in gapped system (2+1)d. The procedure has been well-understood for finite group, which leads to new phase with emergent gauge structure and can be described algebraically using mathematical framework modular tensor category (MTC). develop categorical description MTC, taking into account dynamics field absent group case. When ungauged non-zero Hall conductance, gauged theory remains we determine complete set anyon data theory. On other hand, when conductance vanishes, argue that same effect condensing special Abelian nucleated by inserting 2\pi 2π flux. apply our SU(2) _k display="inline">k MTCs derive full MTC \mathbb{Z}_k display="inline">ℤk parafermion MTCs. also discuss dual emerges after original an is gauged.