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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.
D. Delmastro and J. Gomis, “Symmetries of Abelian Chern-Simons Theories and Arithmetic,” arXiv:1904.12884 [hep-th]
Original
1904
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.
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. Ang, K. Roumpedakis, and S. Seifnashri, “Line Operators of Gauge Theories on Non-Spin Manifolds,” JHEP
Original
1911
Earlier work this paper cites.
Y. Tanizaki and M. Ünsal, “Modified instanton sum in QCD and higher-groups,” JHEP
Original
1912
Earlier work this paper cites.
J. H. C. Whitehead, “On Simply Connected, 4-dimensional Polyhedra,” Commentarii Mathematici Helvetici
1949
Earlier work this paper cites.
M. F. Atiyah, “Riemann surfaces and spin structures,” Annales scientifiques de l’École Normale Supérieure
1971
Earlier work this paper cites.
Princeton mathematical series. Princeton University Press, 1989
H. Lawson and M. Michelsohn, Spin Geometry · 1989
Earlier work this paper cites.
R. Dijkgraaf, C. Vafa, E. P. Verlinde, and H. L. Verlinde, “The Operator Algebra of Orbifold Models,” Commun. Math. Phys
Original
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.
Cambridge University Press, 1991
R. Kirby and L. Taylor, Pin structures on low-dimensional manifolds · 1991
Earlier work this paper cites.
C. Vafa and E. Witten, “On orbifolds with discrete torsion,” J. Geom. Phys
1995
Earlier work this paper cites.
D. Tambara and S. Yamagami, “Tensor categories with fusion rules of self-duality for finite abelian groups,” J.Algebra 209 (1998) 692-707
1998
Earlier work this paper cites.
A. Y. Kitaev, “Unpaired Majorana fermions in quantum wires,” Phys. Usp
2001
Earlier work this paper cites.
M. Berg, C. DeWitt-Morette, S. Gwo, and E. Kramer, “The Pin Groups in Physics: C, P and T,” Reviews in Mathematical Physics
2001
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

Algebraic Topology. Cambridge University Press, 2002
A. Hatcher, Algebraic Topology · 2002
Cited alongside, same era.
V. V. Varlamov, “Universal coverings of orthogonal groups,” Advances in Applied Clifford Algebras
2004
Cited alongside, same era.
A. Kitaev, “Anyons in an exactly solved model and beyond,” Annals Phys
2006
Cited alongside, same era.
D. S. Freed and G. W. Moore, “Setting the quantum integrand of M-theory,” Commun. Math. Phys
2006
Cited alongside, same era.
N. Seiberg, “Modifying the Sum Over Topological Sectors and Constraints on Supergravity,” JHEP
Original
2010
Cited alongside, same era.
P. Etingof, D. Nikshych, V. Ostrik, and E. Meir, “Fusion Categories and Homotopy Theory,” Quantum Topology

Then

D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP
Original
2015
Later among the works it cites.
A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, “Fermionic Symmetry Protected Topological Phases and Cobordisms,” JHEP
Original
2015
Later among the works it cites.
J. C. Teo, T. L. Hughes, and E. Fradkin, “Theory of twist liquids: Gauging an anyonic symmetry,” Annals of Physics
2015
Later among the works it cites.
M. Cheng, “Symmetry fractionalization in three-dimensional ℤ 2 \mathbb{Z}_{2} topological order and fermionic symmetry-protected phases,” 2015
2015
Later among the works it cites.
X. Chen and M. Hermele, “Symmetry fractionalization and anomaly detection in three-dimensional topological phases,” Physical Review B
2016

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2020

Discrete Theta Angles, Symmetries and Anomalies

Hsin, Po-Shen, Lam, Ho Tat

Understand

Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional symmetry protected topological (SPT) phase.

We discuss how the global symmetry and 't Hooft anomaly depends on the discrete theta angles by coupling the gauge theory to a topological quantum field theory (TQFT).
We observe that gauging an Abelian subgroup symmetry, that participates in symmetry extension, with an additional SPT phase leads to a new theory with an emergent Abelian symmetry that also participates in a symmetry extension.
The symmetry extension of the gauge theory is controlled by the discrete theta angle which comes from the SPT phase.

Built on

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.
D. Delmastro and J. Gomis, “Symmetries of Abelian Chern-Simons Theories and Arithmetic,” arXiv:1904.12884 [hep-th]
Original
1904
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.
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. Ang, K. Roumpedakis, and S. Seifnashri, “Line Operators of Gauge Theories on Non-Spin Manifolds,” JHEP
Original
1911
Earlier work this paper cites.
Y. Tanizaki and M. Ünsal, “Modified instanton sum in QCD and higher-groups,” JHEP
Original
1912
Earlier work this paper cites.
J. H. C. Whitehead, “On Simply Connected, 4-dimensional Polyhedra,” Commentarii Mathematici Helvetici
1949
Earlier work this paper cites.
M. F. Atiyah, “Riemann surfaces and spin structures,” Annales scientifiques de l’École Normale Supérieure
1971
Earlier work this paper cites.
Princeton mathematical series. Princeton University Press, 1989
H. Lawson and M. Michelsohn, Spin Geometry · 1989
Earlier work this paper cites.
R. Dijkgraaf, C. Vafa, E. P. Verlinde, and H. L. Verlinde, “The Operator Algebra of Orbifold Models,” Commun. Math. Phys
Original
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.
Cambridge University Press, 1991
R. Kirby and L. Taylor, Pin structures on low-dimensional manifolds · 1991
Earlier work this paper cites.
C. Vafa and E. Witten, “On orbifolds with discrete torsion,” J. Geom. Phys
1995
Earlier work this paper cites.
D. Tambara and S. Yamagami, “Tensor categories with fusion rules of self-duality for finite abelian groups,” J.Algebra 209 (1998) 692-707
1998
Earlier work this paper cites.
A. Y. Kitaev, “Unpaired Majorana fermions in quantum wires,” Phys. Usp
2001
Earlier work this paper cites.
M. Berg, C. DeWitt-Morette, S. Gwo, and E. Kramer, “The Pin Groups in Physics: C, P and T,” Reviews in Mathematical Physics
2001
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

Algebraic Topology. Cambridge University Press, 2002
A. Hatcher, Algebraic Topology · 2002
Cited alongside, same era.
V. V. Varlamov, “Universal coverings of orthogonal groups,” Advances in Applied Clifford Algebras
2004
Cited alongside, same era.
A. Kitaev, “Anyons in an exactly solved model and beyond,” Annals Phys
2006
Cited alongside, same era.
D. S. Freed and G. W. Moore, “Setting the quantum integrand of M-theory,” Commun. Math. Phys
2006
Cited alongside, same era.
N. Seiberg, “Modifying the Sum Over Topological Sectors and Constraints on Supergravity,” JHEP
Original
2010
Cited alongside, same era.
P. Etingof, D. Nikshych, V. Ostrik, and E. Meir, “Fusion Categories and Homotopy Theory,” Quantum Topology

Then

D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP
Original
2015
Later among the works it cites.
A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, “Fermionic Symmetry Protected Topological Phases and Cobordisms,” JHEP
Original
2015
Later among the works it cites.
J. C. Teo, T. L. Hughes, and E. Fradkin, “Theory of twist liquids: Gauging an anyonic symmetry,” Annals of Physics
2015
Later among the works it cites.
M. Cheng, “Symmetry fractionalization in three-dimensional ℤ 2 \mathbb{Z}_{2} topological order and fermionic symmetry-protected phases,” 2015
2015
Later among the works it cites.
X. Chen and M. Hermele, “Symmetry fractionalization and anomaly detection in three-dimensional topological phases,” Physical Review B
2016