From orbifolding conformal field theories to gauging topological phases

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 con...

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Bibliographic Details
Published in:Physical review. B 2017-09, Vol.96 (11), Article 115447
Main Authors: Chen, Xiao, Roy, Abhishek, Teo, Jeffrey C. Y., Ryu, Shinsei
Format: Article
Language:English
Subjects:
Boundary conditions
Braiding
Field theory
Gaging
Gauge theory
Partitions (mathematics)
Phases
Quantum theory
Symmetry
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Summary: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 ZN gauge theory, the twofold symmetric SU(3)1, and the S3-symmetric SO(8)1 Wess-Zumino-Witten theories.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.96.115447