From orbifolding conformal field theories to gauging topological phases

Abstract

Topological phases of matter in (2+1) dimensions are commonly equipped with global symmetries, such as electric-magnetic duality in gauge theories and bilayer symmetry in fractional quantum Hall states. Gauging these symmetries into local dynamical ones is one way of obtaining exotic phases from conventional systems. We study this using the bulk-boundary correspondence and applying the orbifold construction to the (1+1) dimensional edge described by a conformal field theory (CFT). Our procedure puts twisted boundary conditions into the partition function, and predicts the fusion, spin and braiding behavior of anyonic excitations after gauging. We demonstrate this for the electric-magnetic self-dual ${\mathbb{Z}}_N$ gauge theory, the twofold symmetric $SU(3{)}_1$, and the $S_3$-symmetric $SO(8{)}_1$ Wess-Zumino-Witten theories.

23 pages, 1 figure

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• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• Gauging (3+1)-dimensional topological phases: an approach from surface theories
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Dihedral twist liquid models from emergent Majorana fermions
• Twofold twist defect chains at criticality
• Partial fillings of the bosonic $E_8$ quantum Hall state
• Microscopic theory of field-tuned topological transitions in the Kitaev honeycomb model