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Title: Gauging U(1) symmetry in (2+1)d topological phases
We study the gauging of a global U(1) symmetry in a gapped system in(2+1)d. The gauging procedure has been well-understood for a finiteglobal symmetry group, which leads to a new gapped phase with emergentgauge structure and can be described algebraically using themathematical framework of modular tensor category (MTC). We develop acategorical description of U(1) gauging in a MTC, taking into accountthe dynamics of U(1) gauge field absent in the finite group case. Whenthe ungauged system has a non-zero Hall conductance, the gauged theoryremains gapped and we determine the complete set of anyon data for thegauged theory. On the other hand, when the Hall conductance vanishes, weargue that gauging has the same effect of condensing a special Abeliananyon nucleated by inserting 2\pi 2 π U(1) flux. We apply our procedure to theSU(2) _k k MTCs and derive the full MTC data for the \mathbb{Z}_k ℤ k parafermion MTCs. We also discuss a dual U(1) symmetry that emergesafter the original U(1) symmetry of an MTC is gauged.  more » « less
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SciPost Physics
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National Science Foundation
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