Built on

A. Karch, D. Tong, and C. Turner, “A Web of 2d Dualities: 𝐙 2 {\bf Z}_{2} Gauge Fields and Arf Invariants,” SciPost Phys
Original
1902
Earlier work this paper cites.
P.-S. Hsin and A. Turzillo, “Symmetry-Enriched Quantum Spin Liquids in ( 3 + 1 ) d (3+1)d ,” arXiv:1904.11550 [cond-mat.str-el]
Original
1904
Earlier work this paper cites.
Z. Wan, J. Wang, and Y. Zheng, “Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory,” arXiv:1904.00994 [hep-th]
Original
1904
Earlier work this paper cites.
S.-Q. Ning, L. Zou, and M. Cheng, “Fractionalization and Anomalies in Symmetry-Enriched U(1) Gauge Theories,” arXiv:1905.03276 [cond-mat.str-el]
Original
1905
Earlier work this paper cites.
A. Armoni, T. T. Dumitrescu, G. Festuccia, and Z. Komargodski, “Metastable Vacua in Large- N N QCD 3 ,” arXiv:1905.01797 [hep-th]
Original
1905
Earlier work this paper cites.
M. Barkeshli and M. Cheng, “Relative Anomalies in (2+1)D Symmetry Enriched Topological States,” arXiv:1906.10691 [cond-mat.str-el]
Original
1906
Earlier work this paper cites.
W. Ji, S.-H. Shao, and X.-G. Wen, “Topological Transition on the Conformal Manifold,” arXiv:1909.01425 [cond-mat.str-el]
Original
1909
Earlier work this paper cites.
J. H. C. Whitehead, “On Simply Connected, 4-dimensional Polyhedra,” Commentarii Mathematici Helvetici
1949
Earlier work this paper cites.
R. Thom, “Quelques propriétés globales des variétés différentiables.,” Commentarii mathematici Helvetici
1954
Earlier work this paper cites.
E. Thomas, “On the cohomology of the real grassmann complexes and the characteristic classes of n-plane bundles,” Transactions of the American Mathematical Society
1960
Earlier work this paper cites.
S. C. Zhang, T. H. Hansson, and S. Kivelson, “An effective field theory model for the fractional quantum hall effect,” Phys. Rev. Lett
1988
Earlier work this paper cites.
E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun. Math. Phys
1988
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Classical and Quantum Conformal Field Theory,” Commun. Math. Phys
1989
Earlier work this paper cites.
A. N. Schellekens and S. Yankielowicz, “Extended Chiral Algebras and Modular Invariant Partition Functions,” Nucl. Phys
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Naturality in Conformal Field Theory,” Nucl. Phys
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Taming the Conformal Zoo,” Phys. Lett
1989
Earlier work this paper cites.
R. Dijkgraaf and E. Witten, “Topological Gauge Theories and Group Cohomology,” Commun. Math. Phys
1990
Earlier work this paper cites.
A. N. Schellekens and S. Yankielowicz, “Simple Currents, Modular Invariants and Fixed Points,” Int. J. Mod. Phys
1990
Earlier work this paper cites.
J. M. Maldacena, G. W. Moore, and N. Seiberg, “D-brane charges in five-brane backgrounds,” JHEP
2001
Earlier work this paper cites.

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Then

J. C. Y. Teo, T. L. Hughes, and E. Fradkin, “Theory of Twist Liquids: Gauging an Anyonic Symmetry,” Annals Phys
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2015
Later among the works it cites.
A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, “Fermionic Symmetry Protected Topological Phases and Cobordisms,” JHEP
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Later among the works it cites.
C. Wang and T. Senthil, “Time-Reversal Symmetric U ⁡ ( 1 ) U(1) Quantum Spin Liquids,” Phys. Rev
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2016
Later among the works it cites.
N. Tarantino, N. H. Lindner, and L. Fidkowski, “Symmetry fractionalization and twist defects,” New Journal of Physics
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Later among the works it cites.
D. Gaiotto and A. Kapustin, “Spin TQFTs and fermionic phases of matter,” Int. J. Mod. Phys

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2019

Lorentz Symmetry Fractionalization and Dualities in (2+1)d

Hsin, Po-Shen, Shao, Shu-Heng

Understand

We discuss symmetry fractionalization of the Lorentz group in (2+1)$d$ non-spin quantum field theory (QFT), and its implications for dualities.

We prove that two inequivalent non-spin QFTs are dual as spin QFTs if and only if they are related by a Lorentz symmetry fractionalization with respect to an anomalous $\mathbb{Z}_2$ one-form symmetry.
Moreover, if the framing anomalies of two non-spin QFTs differ by a multiple of 8, then they are dual as spin QFTs if and only if they are also dual as non-spin QFTs.
Applications to summing over the spin structures, time-reversal symmetry, and level/rank dualities are explored.

Built on

A. Karch, D. Tong, and C. Turner, “A Web of 2d Dualities: 𝐙 2 {\bf Z}_{2} Gauge Fields and Arf Invariants,” SciPost Phys
Original
1902
Earlier work this paper cites.
P.-S. Hsin and A. Turzillo, “Symmetry-Enriched Quantum Spin Liquids in ( 3 + 1 ) d (3+1)d ,” arXiv:1904.11550 [cond-mat.str-el]
Original
1904
Earlier work this paper cites.
Z. Wan, J. Wang, and Y. Zheng, “Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory,” arXiv:1904.00994 [hep-th]
Original
1904
Earlier work this paper cites.
S.-Q. Ning, L. Zou, and M. Cheng, “Fractionalization and Anomalies in Symmetry-Enriched U(1) Gauge Theories,” arXiv:1905.03276 [cond-mat.str-el]
Original
1905
Earlier work this paper cites.
A. Armoni, T. T. Dumitrescu, G. Festuccia, and Z. Komargodski, “Metastable Vacua in Large- N N QCD 3 ,” arXiv:1905.01797 [hep-th]
Original
1905
Earlier work this paper cites.
M. Barkeshli and M. Cheng, “Relative Anomalies in (2+1)D Symmetry Enriched Topological States,” arXiv:1906.10691 [cond-mat.str-el]
Original
1906
Earlier work this paper cites.
W. Ji, S.-H. Shao, and X.-G. Wen, “Topological Transition on the Conformal Manifold,” arXiv:1909.01425 [cond-mat.str-el]
Original
1909
Earlier work this paper cites.
J. H. C. Whitehead, “On Simply Connected, 4-dimensional Polyhedra,” Commentarii Mathematici Helvetici
1949
Earlier work this paper cites.
R. Thom, “Quelques propriétés globales des variétés différentiables.,” Commentarii mathematici Helvetici
1954
Earlier work this paper cites.
E. Thomas, “On the cohomology of the real grassmann complexes and the characteristic classes of n-plane bundles,” Transactions of the American Mathematical Society
1960
Earlier work this paper cites.
S. C. Zhang, T. H. Hansson, and S. Kivelson, “An effective field theory model for the fractional quantum hall effect,” Phys. Rev. Lett
1988
Earlier work this paper cites.
E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun. Math. Phys
1988
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Classical and Quantum Conformal Field Theory,” Commun. Math. Phys
1989
Earlier work this paper cites.
A. N. Schellekens and S. Yankielowicz, “Extended Chiral Algebras and Modular Invariant Partition Functions,” Nucl. Phys
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Naturality in Conformal Field Theory,” Nucl. Phys
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Taming the Conformal Zoo,” Phys. Lett
1989
Earlier work this paper cites.
R. Dijkgraaf and E. Witten, “Topological Gauge Theories and Group Cohomology,” Commun. Math. Phys
1990
Earlier work this paper cites.
A. N. Schellekens and S. Yankielowicz, “Simple Currents, Modular Invariants and Fixed Points,” Int. J. Mod. Phys
1990
Earlier work this paper cites.
J. M. Maldacena, G. W. Moore, and N. Seiberg, “D-brane charges in five-brane backgrounds,” JHEP
2001
Earlier work this paper cites.

Similar

J. Fuchs, I. Runkel, and C. Schweigert, “TFT construction of RCFT correlators. 3. Simple currents,” Nucl. Phys
2004
Cited alongside, same era.
A. Kitaev, “Anyons in an exactly solved model and beyond,” Annals Phys
2006
Cited alongside, same era.
E. Rowell, R. Stong, and Z. Wang, “On classification of modular tensor categories,” Communications in Mathematical Physics
2009
Cited alongside, same era.
P. Etingof, D. Nikshych, V. Ostrik, and E. Meir, “Fusion Categories and Homotopy Theory,” Quantum Topology
Original
2010
Cited alongside, same era.
T. Banks and N. Seiberg, “Symmetries and Strings in Field Theory and Gravity,” Phys. Rev
Original
2011
Cited alongside, same era.