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We review the properties of orbifold operations on two-dimensional quantum field theories, either bosonic or fermionic, and describe the "Orbifold groupoids" which control the composition of orbifold operations.
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2014
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N. Carqueville and I. Runkel, Orbifold completion of defect bicategories
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D. Gaiotto, A. Kapustin, Z. Komargodski, and N. Seiberg, Theta, time reversal and temperature
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L. Bhardwaj and Y. Tachikawa, On finite symmetries and their gauging in two dimensions
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2019
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D. Gaiotto and T. Johnson-Freyd, Symmetry Protected Topological phases and Generalized Cohomology
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T. Johnson-Freyd, The Moonshine Anomaly
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T. Senthil, D. T. Son, C. Wang, and C. Xu, Duality between (2+1)d quantum critical points
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