Built on

A. N. Redlich, “Parity Violation and Gauge Noninvariance of the Effective Gauge Field Action in Three-Dimensions,” Phys. Rev
1984
Earlier work this paper cites.
L. Alvarez-Gaume, S. Della Pietra, and G. W. Moore, “Anomalies and Odd Dimensions,” Annals Phys
1985
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.
C. Wang and T. Senthil, “Boson topological insulators: A window into highly entangled quantum phases,” Phys. Rev
Original
2013
Earlier work this paper cites.
P. Bonderson, C. Nayak, and X.-L. Qi, “A time-reversal invariant topological phase at the surface of a 3D topological insulator,” J. Stat. Mech
Original
2013
Earlier work this paper cites.
X. Chen, L. Fidkowski, and A. Vishwanath, “Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator,” Phys. Rev
Original
2014
Earlier work this paper cites.
C. Wang and T. Senthil, “Interacting fermionic topological insulators/superconductors in three dimensions,” Phys. Rev
Original
2015
Earlier work this paper cites.
A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, “Fermionic Symmetry Protected Topological Phases and Cobordisms,” JHEP
Original
2015
Earlier work this paper cites.
C. Xu and Y.-Z. You, “Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator,” Phys. Rev
Original
2015
Earlier work this paper cites.

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D. T. Son, “Is the Composite Fermion a Dirac Particle?,” Phys. Rev
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D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP
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Cited alongside, same era.
E. Witten, “Fermion Path Integrals And Topological Phases,” Rev. Mod. Phys
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2017

Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$

Cordova, Clay, Hsin, Po-Shen, Seiberg, Nathan

Understand

We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry $\cal T$.

The standard relation ${\cal T}^2=(-1)^F$ is satisfied on all the "perturbative operators" i.e.
polynomials in the fundamental fields and their derivatives.
However, we find that it is often the case that acting on more complicated operators ${\cal T}^2=(-1)^F {\cal M}$ with $\cal M$ a non-trivial global symmetry.

Built on

A. N. Redlich, “Parity Violation and Gauge Noninvariance of the Effective Gauge Field Action in Three-Dimensions,” Phys. Rev
1984
Earlier work this paper cites.
L. Alvarez-Gaume, S. Della Pietra, and G. W. Moore, “Anomalies and Odd Dimensions,” Annals Phys
1985
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.
C. Wang and T. Senthil, “Boson topological insulators: A window into highly entangled quantum phases,” Phys. Rev
Original
2013
Earlier work this paper cites.
P. Bonderson, C. Nayak, and X.-L. Qi, “A time-reversal invariant topological phase at the surface of a 3D topological insulator,” J. Stat. Mech
Original
2013
Earlier work this paper cites.
X. Chen, L. Fidkowski, and A. Vishwanath, “Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator,” Phys. Rev
Original
2014
Earlier work this paper cites.
C. Wang and T. Senthil, “Interacting fermionic topological insulators/superconductors in three dimensions,” Phys. Rev
Original
2015
Earlier work this paper cites.
A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, “Fermionic Symmetry Protected Topological Phases and Cobordisms,” JHEP
Original
2015
Earlier work this paper cites.
C. Xu and Y.-Z. You, “Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator,” Phys. Rev
Original
2015
Earlier work this paper cites.

Similar

D. T. Son, “Is the Composite Fermion a Dirac Particle?,” Phys. Rev
Original
2015
Cited alongside, same era.
C. Wang and T. Senthil, “Dual Dirac Liquid on the Surface of the Electron Topological Insulator,” Phys. Rev
Original
2015
Cited alongside, same era.
D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP
Original
2015
Cited alongside, same era.
E. Witten, “Fermion Path Integrals And Topological Phases,” Rev. Mod. Phys
Original
2016
Cited alongside, same era.
E. Witten, “The ”Parity” Anomaly On An Unorientable Manifold,” Phys. Rev
Original

Then

Beyond the bibliography

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

Open on alphaXiv

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2016

Cited alongside, same era.

M. A. Metlitski and A. Vishwanath, “Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators,” Phys. Rev

Original

2016

Cited alongside, same era.

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

Original

2016

Cited alongside, same era.

N. Seiberg and E. Witten, “Gapped Boundary Phases of Topological Insulators via Weak Coupling,” PTEP

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2016

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N. Seiberg, T. Senthil, C. Wang, and E. Witten, “A Duality Web in 2+1 Dimensions and Condensed Matter Physics,” Annals Phys

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2016

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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.

A. Kapustin, “Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology,” arXiv:1403.1467 [cond-mat.str-el]

Original

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M. Barkeshli, P. Bonderson, C.-M. Jian, M. Cheng, and K. Walker, “Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies,” arXiv:1612.07792 [cond-mat.str-el]

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