Built on

Y. H. Lin and S. H. Shao, “Anomalies and Bounds on Charged Operators,” arXiv:1904.04833 [hep-th]
Original
1904
Earlier work this paper cites.
Y. Zhou, “ 3 d 3d One-form Mixed Anomaly and Entanglement Entropy,” arXiv:1904.06924 [hep-th]
Original
1904
Earlier work this paper cites.
W. Ji and X. G. Wen, “Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions,” arXiv:1905.13279 [cond-mat.str-el]
Original
1905
Earlier work this paper cites.
J. Wess and B. Zumino, “Consequences of anomalous Ward identities,” Phys. Lett. 37B
1971
Earlier work this paper cites.
G. ’t Hooft, “Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking,” NATO Sci. Ser. B 59
1980
Earlier work this paper cites.
L. D. Faddeev and S. L. Shatashvili, “Algebraic and Hamiltonian Methods in the Theory of Nonabelian Anomalies,” Theor. Math. Phys. 60
1984
Earlier work this paper cites.
C. G. Callan, Jr. and J. A. Harvey, “Anomalies and Fermion Zero Modes on Strings and Domain Walls,” Nucl. Phys. B 250
1985
Earlier work this paper cites.
C. Vafa, “Modular Invariance and Discrete Torsion on Orbifolds,” Nucl. Phys. B 273
1987
Earlier work this paper cites.
E. P. Verlinde, “Fusion Rules and Modular Transformations in 2D Conformal Field Theory,” Nucl. Phys. B 300
1988
Earlier work this paper cites.
E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun. Math. Phys. 121
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Classical and Quantum Conformal Field Theory,” Commun. Math. Phys. 123
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Taming the Conformal Zoo,” Phys. Lett. B 220
1989
Earlier work this paper cites.
J. L. Cardy, “Boundary Conditions, Fusion Rules and the Verlinde Formula,” Nucl. Phys. B 324
1989
Earlier work this paper cites.

Similar

N. Ishibashi, “The Boundary and Crosscap States in Conformal Field Theories,” Mod. Phys. Lett. A 4
1989
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2001
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J. Fuchs, I. Runkel and C. Schweigert, “TFT construction of RCFT correlators 1. Partition functions,” Nucl. Phys. B 646
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J. Frohlich, J. Fuchs, I. Runkel and C. Schweigert, “Kramers-Wannier duality from conformal defects,” Phys. Rev. Lett. 93
2004
Cited alongside, same era.

Then

X. Chen, Z. C. Gu, Z. X. Liu and X. G. Wen, “Symmetry protected topological orders and the group cohomology of their symmetry group,” Phys. Rev. B 87
Original
2013
Later among the works it cites.
L. Y. Hung and X. G. Wen, “Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases,” Phys. Rev. B 87
Original
2013
Later among the works it cites.
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, “Generalized Global Symmetries,” JHEP 1502
Original
2015
Later among the works it cites.
D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg, “Theta, Time Reversal, and Temperature,” JHEP 1705
Original
2017
Later among the works it cites.
B. Han, A. Tiwari, C. T. Hsieh and S. Ryu, “Boundary conformal field theory and symmetry protected topological phases in 2 + 1 2+1 dimensions,” Phys. Rev. B 96

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2019

Two-dimensional Anomaly, Orbifolding, and Boundary States

Kikuchi, Ken, Zhou, Yang

Understand

We study anomalies of discrete internal global symmetry $G$ in two-dimensional rational conformal field theories based on twisted torus partition functions.

The anomaly of $G$ can be seen from the noncommutativity of two symmetry lines inserted along the nontrivial cycles of two-torus and we propose a criterion to detect the anomaly, which agrees with the truncated modular $S$-matrix approach.
The obstruction for orbifolding has been recently interpreted as a mixed anomaly between $G$ and large diffeomorphisms.
We clarify the relations among anomaly-free conditions, orbifoldable conditions, and invariant boundary state condition, focusing on Wess-Zumino-Witten models.

Built on

Y. H. Lin and S. H. Shao, “Anomalies and Bounds on Charged Operators,” arXiv:1904.04833 [hep-th]
Original
1904
Earlier work this paper cites.
Y. Zhou, “ 3 d 3d One-form Mixed Anomaly and Entanglement Entropy,” arXiv:1904.06924 [hep-th]
Original
1904
Earlier work this paper cites.
W. Ji and X. G. Wen, “Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions,” arXiv:1905.13279 [cond-mat.str-el]
Original
1905
Earlier work this paper cites.
J. Wess and B. Zumino, “Consequences of anomalous Ward identities,” Phys. Lett. 37B
1971
Earlier work this paper cites.
G. ’t Hooft, “Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking,” NATO Sci. Ser. B 59
1980
Earlier work this paper cites.
L. D. Faddeev and S. L. Shatashvili, “Algebraic and Hamiltonian Methods in the Theory of Nonabelian Anomalies,” Theor. Math. Phys. 60
1984
Earlier work this paper cites.
C. G. Callan, Jr. and J. A. Harvey, “Anomalies and Fermion Zero Modes on Strings and Domain Walls,” Nucl. Phys. B 250
1985
Earlier work this paper cites.
C. Vafa, “Modular Invariance and Discrete Torsion on Orbifolds,” Nucl. Phys. B 273
1987
Earlier work this paper cites.
E. P. Verlinde, “Fusion Rules and Modular Transformations in 2D Conformal Field Theory,” Nucl. Phys. B 300
1988
Earlier work this paper cites.
E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun. Math. Phys. 121
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Classical and Quantum Conformal Field Theory,” Commun. Math. Phys. 123
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Taming the Conformal Zoo,” Phys. Lett. B 220
1989
Earlier work this paper cites.
J. L. Cardy, “Boundary Conditions, Fusion Rules and the Verlinde Formula,” Nucl. Phys. B 324
1989
Earlier work this paper cites.

Similar

N. Ishibashi, “The Boundary and Crosscap States in Conformal Field Theories,” Mod. Phys. Lett. A 4
1989
Cited alongside, same era.
V. B. Petkova and J. B. Zuber, “Generalized twisted partition functions,” Phys. Lett. B 504
2001
Cited alongside, same era.
J. Fuchs, I. Runkel and C. Schweigert, “TFT construction of RCFT correlators 1. Partition functions,” Nucl. Phys. B 646
2002
Cited alongside, same era.
J. Fuchs, I. Runkel and C. Schweigert, “TFT construction of RCFT correlators. 2. Unoriented world sheets,” Nucl. Phys. B 678
2003
Cited alongside, same era.
J. Frohlich, J. Fuchs, I. Runkel and C. Schweigert, “Kramers-Wannier duality from conformal defects,” Phys. Rev. Lett. 93
2004
Cited alongside, same era.

Then

X. Chen, Z. C. Gu, Z. X. Liu and X. G. Wen, “Symmetry protected topological orders and the group cohomology of their symmetry group,” Phys. Rev. B 87
Original
2013
Later among the works it cites.
L. Y. Hung and X. G. Wen, “Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases,” Phys. Rev. B 87
Original
2013
Later among the works it cites.
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, “Generalized Global Symmetries,” JHEP 1502
Original
2015
Later among the works it cites.
D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg, “Theta, Time Reversal, and Temperature,” JHEP 1705
Original
2017
Later among the works it cites.
B. Han, A. Tiwari, C. T. Hsieh and S. Ryu, “Boundary conformal field theory and symmetry protected topological phases in 2 + 1 2+1 dimensions,” Phys. Rev. B 96

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

J. Fuchs, I. Runkel and C. Schweigert, “TFT construction of RCFT correlators. 3. Simple currents,” Nucl. Phys. B 694

2004

Cited alongside, same era.

J. Fuchs, I. Runkel and C. Schweigert, “TFT construction of RCFT correlators IV: Structure constants and correlation functions,” Nucl. Phys. B 715

2005

Cited alongside, same era.

J. Fjelstad, J. Fuchs, I. Runkel and C. Schweigert, “TFT construction of RCFT correlators. V. Proof of modular invariance and factorisation,” Theor. Appl. Categor. 16

2006

Cited alongside, same era.

J. Frohlich, J. Fuchs, I. Runkel and C. Schweigert, “Duality and defects in rational conformal field theory,” Nucl. Phys. B 763

2006

Cited alongside, same era.

J. Frohlich, J. Fuchs, I. Runkel and C. Schweigert, “Duality and defects in rational conformal field theory,” Nucl. Phys. B 763

2006

Cited alongside, same era.

I. Runkel, J. Fjelstad, J. Fuchs and C. Schweigert, “Topological and conformal field theory as Frobenius algebras,” Contemp. Math. 431

2007

Cited alongside, same era.

A. Davydov, L. Kong and I. Runkel, “Invertible Defects and Isomorphisms of Rational CFTs,” Adv. Theor. Math. Phys. 15