Built on

G. W. Moore and N. Seiberg, “Classical and Quantum Conformal Field Theory,” Commun. Math. Phys
1989
Earlier work this paper cites.
E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun. Math. Phys
1989
Earlier work this paper cites.
World Scientific, 1990
G. W. Moore and N. Seiberg, “Lectures on RCFT,” in Strings ’89, Proceedings of the Trieste Spring School on Superstrings · 1990
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.
X.-z. Dai and D. S. Freed, “eta invariants and determinant lines,” J. Math. Phys
2001
Earlier work this paper cites.
L. Fidkowski, X. Chen, and A. Vishwanath, “Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model,” Phys. Rev
Original
2013
Earlier work this paper cites.
X.-G. Wen, “Classifying gauge anomalies through symmetry-protected trivial orders and classifying gravitational anomalies through topological orders,” Phys. Rev
Original
2013
Earlier work this paper cites.

Similar

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
Original
2013
Cited alongside, same era.
A. Kapustin and R. Thorngren, “Anomalies of discrete symmetries in three dimensions and group cohomology,” Phys. Rev. Lett
Original
2014
Cited alongside, same era.
M. Dierigl and A. Pritzel, “Topological Model for Domain Walls in (Super-)Yang-Mills Theories,” Phys. Rev
Original
2014
Cited alongside, same era.
C. Wang and T. Senthil, “Interacting Fermionic Topological Insulators/Superconductors in Three Dimensions,” Phys. Rev
Original
2015
Cited alongside, same era.
T. Morimoto, A. Furusaki, and C. Mudry, “Breakdown of the topological classification ℤ \mathbb{Z} for gapped phases of noninteracting fermions by quartic interactions,” Phys. Rev

Then

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.
D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP
Original
2015
Later among the works it cites.
E. Witten, “Fermion Path Integrals And Topological Phases,” Rev. Mod. Phys
Original
2016
Closest in time.
C.-T. Hsieh, G. Y. Cho, and S. Ryu, “Global Anomalies on the Surface of Fermionic Symmetry-Protected Topological Phases in (3+1) Dimensions,” Phys. Rev
Original
2016
Closest in time.
A. P. O. Chan, J. C. Y. Teo, and S. Ryu, “Topological Phases on Non-Orientable Surfaces: Twisting by Parity Symmetry,” New J. Phys

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2016

On time-reversal anomaly of 2+1d topological phases

Tachikawa, Yuji, Yonekura, Kazuya

Understand

We describe a method to find the anomaly of the time-reversal symmetry of 2+1d topological quantum field theories, by computing the fractional anomalous momentum on the cross-cap background.

This allows us, for example, to identify the parameter $\nu$ mod 16 of the bulk 3+1d topological superconductor with $\mathsf{T}^2=(-1)^F$ on whose boundary a given 2+1d time-reversal-invariant topological phase can appear.

Built on

G. W. Moore and N. Seiberg, “Classical and Quantum Conformal Field Theory,” Commun. Math. Phys
1989
Earlier work this paper cites.
E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun. Math. Phys
1989
Earlier work this paper cites.
World Scientific, 1990
G. W. Moore and N. Seiberg, “Lectures on RCFT,” in Strings ’89, Proceedings of the Trieste Spring School on Superstrings · 1990
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.
X.-z. Dai and D. S. Freed, “eta invariants and determinant lines,” J. Math. Phys
2001
Earlier work this paper cites.
L. Fidkowski, X. Chen, and A. Vishwanath, “Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model,” Phys. Rev
Original
2013
Earlier work this paper cites.
X.-G. Wen, “Classifying gauge anomalies through symmetry-protected trivial orders and classifying gravitational anomalies through topological orders,” Phys. Rev
Original
2013
Earlier work this paper cites.

Similar

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
Original
2013
Cited alongside, same era.
A. Kapustin and R. Thorngren, “Anomalies of discrete symmetries in three dimensions and group cohomology,” Phys. Rev. Lett
Original
2014
Cited alongside, same era.
M. Dierigl and A. Pritzel, “Topological Model for Domain Walls in (Super-)Yang-Mills Theories,” Phys. Rev
Original
2014
Cited alongside, same era.
C. Wang and T. Senthil, “Interacting Fermionic Topological Insulators/Superconductors in Three Dimensions,” Phys. Rev
Original
2015
Cited alongside, same era.
T. Morimoto, A. Furusaki, and C. Mudry, “Breakdown of the topological classification ℤ \mathbb{Z} for gapped phases of noninteracting fermions by quartic interactions,” Phys. Rev

Then

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.
D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP
Original
2015
Later among the works it cites.
E. Witten, “Fermion Path Integrals And Topological Phases,” Rev. Mod. Phys
Original
2016
Closest in time.
C.-T. Hsieh, G. Y. Cho, and S. Ryu, “Global Anomalies on the Surface of Fermionic Symmetry-Protected Topological Phases in (3+1) Dimensions,” Phys. Rev
Original
2016
Closest in time.
A. P. O. Chan, J. C. Y. Teo, and S. Ryu, “Topological Phases on Non-Orientable Surfaces: Twisting by Parity Symmetry,” New J. Phys

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Original

2015

Cited alongside, same era.

G. Y. Cho, C.-T. Hsieh, T. Morimoto, and S. Ryu, “Topological Phases Protected by Reflection Symmetry and Cross-Cap States,” Phys. Rev

Original

2015

Cited alongside, same era.

J. C. Wang, Z.-C. Gu, and X.-G. Wen, “Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond,” Phys. Rev. Lett

Original

2015

Cited alongside, same era.

A. Kitaev, “Homotopy-Theoretic Approach to SPT Phases in Action: ℤ 16 \mathbb{Z}_{16} Classification of Three-Dimensional Superconductors,”. Lecture notes available at http://www.ipam.ucla.edu/abstract/?tid=12389&pcode=STQ2015

Cited in the paper.

M. A. Metlitski, L. Fidkowski, X. Chen, and A. Vishwanath, “Interaction Effects on 3D Topological Superconductors: Surface Topological Order from Vortex Condensation, the 16 Fold Way and Fermionic Kramers Doublets,” arXiv:1406.3032 [cond-mat.str-el]

Original

Cited in the paper.

N. Seiberg and E. Witten, “Gapped Boundary Phases of Topological Insulators via Weak Coupling,” arXiv:1602.04251 [cond-mat.str-el]

Original

Cited in the paper.

Y. Tachikawa and K. Yonekura, “Gauge Interactions and Topological Phases of Matter,” arXiv:1604.06184 [hep-th]

Original

Cited in the paper.

E. Witten, “The ‘Parity’ Anomaly on an Unorientable Manifold,” arXiv:1605.02391 [hep-th]

Original