Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$

Z. Wan, J. Wang, and Y. Zheng, “Quantum Yang-Mills 4d Theory and Time-Reversal Symmetric 5d Higher-Gauge TQFT: Anyonic-String/Brane Braiding Statistics to Topological Link Invariants,” Phys. Rev. D

Original

1904

Earlier work this paper cites.

R. Kobayashi, K. Ohmori, and Y. Tachikawa, “On gapped boundaries for SPT phases beyond group cohomology,” arXiv:1905.05391 [cond-mat.str-el]

Original

1905

Earlier work this paper cites.

C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, “Anomalies in the Space of Coupling Constants and Their Dynamical Applications I,” arXiv:1905.09315 [hep-th]

Original

1905

Earlier work this paper cites.

C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, “Anomalies in the Space of Coupling Constants and Their Dynamical Applications II,” arXiv:1905.13361 [hep-th]

Original

1905

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.

C. Córdova and K. Ohmori, “Anomaly Obstructions to Symmetry Preserving Gapped Phases,” arXiv:1910.04962 [hep-th]

Original

1910

Earlier work this paper cites.

J. H. C. Whitehead, “On Simply Connected, 4-dimensional Polyhedra,” Commentarii Mathematici Helvetici

1949

Earlier work this paper cites.

S. L. Adler, “Axial vector vertex in spinor electrodynamics,” Phys. Rev

1969

Earlier work this paper cites.

J. S. Bell and R. Jackiw, “A PCAC puzzle: π 0 → γ ​ γ \pi^{0}\to\gamma\gamma in the σ \sigma model,” Nuovo Cim

1969

Earlier work this paper cites.

M. F. Atiyah and I. M. Singer, “The index of elliptic operators on compact manifolds,” Bull. Am. Math. Soc

1969

Earlier work this paper cites.

J. Wess and B. Zumino, “Consequences of anomalous Ward identities,” Phys. Lett

1971

Earlier work this paper cites.

S. Halperin and D. Toledo, “Stiefel-Whitney Homology Classes,” Annals of Mathematics

1972

Earlier work this paper cites.

Annals of mathematics studies. Princeton University Press, 1974

J. Milnor and J. Stasheff, Characteristic Classes · 1974

Earlier work this paper cites.

A. S. Goldhaber, “Spin and Statistics Connection for Charge-Monopole Composites,” Phys. Rev. Lett

1976

Earlier work this paper cites.

C. Montonen and D. I. Olive, “Magnetic Monopoles as Gauge Particles?,” Phys. Lett

1977

Earlier work this paper cites.

E. Witten, “Dyons of Charge e theta/2 pi,” Phys. Lett

1979

Earlier work this paper cites.

F. Wilczek, “Remarks on Dyons,” Phys. Rev. Lett

1982

Earlier work this paper cites.

A. S. Schwarz, “Field theories with no local conservation of the electric charge,” Nucl. Phys

1982

Earlier work this paper cites.

A. S. Goldhaber, R. MacKenzie, and F. Wilczek, “Field corrections to induced statistics,” Mod. 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.

P. Roche, V. Pasquier, and R. Dijkgraaf, “Quasi Hopf algebras, group cohomology and orbifold models,” Nucl. Phys. Proc. Suppl

1990

Earlier work this paper cites.

M. Bucher, H.-K. Lo, and J. Preskill, “Topological approach to Alice electrodynamics,” Nucl. Phys

1992

Earlier work this paper cites.

E. Witten, “On S duality in Abelian gauge theory,” Selecta Math

1995

Earlier work this paper cites.

A. Coste, T. Gannon, and P. Ruelle, “Finite group modular data,” Nucl. Phys

2000

Earlier work this paper cites.

Cambridge University Press, 2000

A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects · 2000

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.

Algebraic Topology. Cambridge University Press, 2002

A. Hatcher, Algebraic Topology · 2002

Earlier work this paper cites.

J. S. Carter, D. Jelsovsky, S. Kamada, L. Langford, and M. Saito, “Quandle Cohomology and State-Sum Invariants of Knotted Curves and Surfaces,” Transactions of the American Mathematical Society

2003

Earlier work this paper cites.

M. B. Hastings and X.-G. Wen, “Quasi-adiabatic continuation of quantum states: The Stability of topological ground state degeneracy and emergent gauge invariance,” Phys. Rev

2005

Earlier work this paper cites.

M. Ünsal, “Abelian duality, confinement, and chiral symmetry breaking in QCD(adj),” Phys. Rev. Lett

Original

2008

Earlier work this paper cites.

M. Ünsal, “Magnetic bion condensation: A New mechanism of confinement and mass gap in four dimensions,” Phys. Rev

Original

2009

Cited alongside, same era.

J. Maciejko, X.-L. Qi, A. Karch, and S.-C. Zhang, “Fractional topological insulators in three dimensions,” Phys. Rev. Lett

Original

2010

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.

S. Gukov and E. Witten, “Rigid Surface Operators,” Adv. Theor. Math. Phys

Original

2010

Cited alongside, same era.

B. Swingle, M. Barkeshli, J. McGreevy, and T. Senthil, “Correlated Topological Insulators and the Fractional Magnetoelectric Effect,” Phys. Rev

N. Tarantino, N. H. Lindner, and L. Fidkowski, “Symmetry fractionalization and twist defects,” New Journal of Physics

Original

2016

Later among the works it cites.

X. Chen, A. Tiwari, and S. Ryu, “Bulk-boundary correspondence in (3+1)-dimensional topological phases,” Phys. Rev

Original

2016

Later among the works it cites.

X. Chen and M. Hermele, “Symmetry fractionalization and anomaly detection in three-dimensional topological phases,” Phys. Rev

Original

2016

Later among the works it cites.

D. Gaiotto and A. Kapustin, “Spin TQFTs and fermionic phases of matter,” Int. J. Mod. Phys

Original

2016

Later among the works it cites.

P.-S. Hsin and N. Seiberg, “Level/rank Duality and Chern-Simons-Matter Theories,” JHEP