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

Abstract

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

11+10pages; 0+3 figures

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• Fusion 3-Categories for Duality Defects
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Ordering the topological order in the fractional quantum Hall effect
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• Proliferation transitions from a topological phase in $2+1$ dimensions