Built on

A. M. Polyakov, “Compact Gauge Fields And The Infrared Catastrophe,” Phys. Lett. B59
1975
Earlier work this paper cites.
M. F. Atiyah, I. M. Singer, and V. Patodi, “Spectral Asymmetry In Riemannian Geometry,” Math. Proc. Camb. Phil. Soc. 77
1975
Earlier work this paper cites.
R. Jackiw and C. Rebbi, “Solitons With Fermion Number 1/2,” Phys. Rev. D 13
1976
Earlier work this paper cites.
A. N. Redlich, “Parity Violation and Gauge Noninvariance of the Effective Gauge Field Action in Three-Dimensions,” Phys. Rev. D 29
1984
Earlier work this paper cites.
L. Alvarez-Gaumé, S. Della Pietra, and G. Moore, “Anomalies And Odd Dimensions,” Ann. Phys. 163
1985
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. B250
1985
Earlier work this paper cites.
R. Dijkgraaf and E. Witten, “Topological Gauge Theories and Group Cohomology,” Commun. Math. Phys. 129
1990
Earlier work this paper cites.
G. W. Moore and N. Read, “Nonabelions In The Fractional Quantum Hall Effect,” Nucl. Phys. B 360
1991
Earlier work this paper cites.
X. Dai and D. S. Freed, “ η \eta -Invariants And Determinant Lines,” J. Math. Phys. 35
1994
Earlier work this paper cites.
E. Witten, “On Flux Quantization In M Theory And The Effective Action,” J. Geom. Phys. 22
1997
Earlier work this paper cites.
N. Read and D. Green, “Paired States of Fermions in Two Dimensions with Breaking of Parity and Time-Reversal Symmetries, and the Fractional Quantum Hall Effect,” arXiv:cond-mat/9906453, Phys. Rev. B 61
2000
Earlier work this paper cites.

Similar

V. Borokhov, A. Kapustin and X. k. Wu, “Topological Disorder Operators in Three-Dimensional Conformal Field Theory,” JHEP 0211
2002
Cited alongside, same era.
X.-G. Wen, “Quantum Orders And Symmetric Spin Liquids,” Phys. Rev. B65
2002
Cited alongside, same era.
E. Diaconescu, G. Moore, and E. Witten, “ E 8 E_{8} Gauge Theory, and A Derivation Of K-Theory From M-Theory,” Adv. Math. Theor. Phys. 6
Original
2003
Cited alongside, same era.
M. Z. Hasan and C. L. Kane, “Topological Insulators,” Rev. Mod. Phys. 82
2010
Cited alongside, same era.
J. Distler, D. Freed, and G. W. Moore, “Orientifold Precis,” arXiv:0906.0795, in Mathematical Foundations Of Quantum Field Theory and Perturbative String Theory
Original
2011
Cited alongside, same era.

Then

A. M. Essin and M. Hermele, “Classifying Fractionalization: Symmetry Classifiation Of Gapped ℤ 2 {\mathbb{Z}}_{2} Spin Liquids In Two Dimensions,” Phys. Rev. B87
Original
2013
Later among the works it cites.
A. Mesaros and Y. Ran, “A Classification Of Symmetry Enriched Topological Phases With Exactly Solvable Models,” Phys. Rev. B87
Original
2013
Later among the works it cites.
C. Wang and T. Senthil, “Interacting Fermionic Topological Insulators/Superconductors In Three Dimensions,” arXiv:1401.1142, Phys. Rev. B89
Original
2014
Later among the works it cites.
X. Chen, L. Fidkowski and A. Vishwanath, “Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator,” Phys. Rev. B 89
Original
2014
Later among the works it cites.

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Reading the bibliography…

2016

The "Parity" Anomaly On An Unorientable Manifold

Witten, Edward

Understand

The "parity" anomaly -- more accurately described as an anomaly in time-reversal or reflection symmetry -- arises in certain theories of fermions coupled to gauge fields and/or gravity in a spacetime of odd dimension.

This anomaly has traditionally been studied on orientable manifolds only, but recent developments involving topological superconductors have made it clear that one can get more information by asking what happens on an unorientable manifold.
In this paper, we give a full description of the "parity" anomaly for fermions coupled to gauge fields and gravity in $2+1$ dimensions on a possibly unorientable spacetime.
We consider an application to topological superconductors and another application to M-theory.

Built on

A. M. Polyakov, “Compact Gauge Fields And The Infrared Catastrophe,” Phys. Lett. B59
1975
Earlier work this paper cites.
M. F. Atiyah, I. M. Singer, and V. Patodi, “Spectral Asymmetry In Riemannian Geometry,” Math. Proc. Camb. Phil. Soc. 77
1975
Earlier work this paper cites.
R. Jackiw and C. Rebbi, “Solitons With Fermion Number 1/2,” Phys. Rev. D 13
1976
Earlier work this paper cites.
A. N. Redlich, “Parity Violation and Gauge Noninvariance of the Effective Gauge Field Action in Three-Dimensions,” Phys. Rev. D 29
1984
Earlier work this paper cites.
L. Alvarez-Gaumé, S. Della Pietra, and G. Moore, “Anomalies And Odd Dimensions,” Ann. Phys. 163
1985
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. B250
1985
Earlier work this paper cites.
R. Dijkgraaf and E. Witten, “Topological Gauge Theories and Group Cohomology,” Commun. Math. Phys. 129
1990
Earlier work this paper cites.
G. W. Moore and N. Read, “Nonabelions In The Fractional Quantum Hall Effect,” Nucl. Phys. B 360
1991
Earlier work this paper cites.
X. Dai and D. S. Freed, “ η \eta -Invariants And Determinant Lines,” J. Math. Phys. 35
1994
Earlier work this paper cites.
E. Witten, “On Flux Quantization In M Theory And The Effective Action,” J. Geom. Phys. 22
1997
Earlier work this paper cites.
N. Read and D. Green, “Paired States of Fermions in Two Dimensions with Breaking of Parity and Time-Reversal Symmetries, and the Fractional Quantum Hall Effect,” arXiv:cond-mat/9906453, Phys. Rev. B 61
2000
Earlier work this paper cites.

Similar

V. Borokhov, A. Kapustin and X. k. Wu, “Topological Disorder Operators in Three-Dimensional Conformal Field Theory,” JHEP 0211
2002
Cited alongside, same era.
X.-G. Wen, “Quantum Orders And Symmetric Spin Liquids,” Phys. Rev. B65
2002
Cited alongside, same era.
E. Diaconescu, G. Moore, and E. Witten, “ E 8 E_{8} Gauge Theory, and A Derivation Of K-Theory From M-Theory,” Adv. Math. Theor. Phys. 6
Original
2003
Cited alongside, same era.
M. Z. Hasan and C. L. Kane, “Topological Insulators,” Rev. Mod. Phys. 82
2010
Cited alongside, same era.
J. Distler, D. Freed, and G. W. Moore, “Orientifold Precis,” arXiv:0906.0795, in Mathematical Foundations Of Quantum Field Theory and Perturbative String Theory
Original
2011
Cited alongside, same era.

Then

A. M. Essin and M. Hermele, “Classifying Fractionalization: Symmetry Classifiation Of Gapped ℤ 2 {\mathbb{Z}}_{2} Spin Liquids In Two Dimensions,” Phys. Rev. B87
Original
2013
Later among the works it cites.
A. Mesaros and Y. Ran, “A Classification Of Symmetry Enriched Topological Phases With Exactly Solvable Models,” Phys. Rev. B87
Original
2013
Later among the works it cites.
C. Wang and T. Senthil, “Interacting Fermionic Topological Insulators/Superconductors In Three Dimensions,” arXiv:1401.1142, Phys. Rev. B89
Original
2014
Later among the works it cites.
X. Chen, L. Fidkowski and A. Vishwanath, “Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator,” Phys. Rev. B 89
Original
2014
Later among the works it cites.

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

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. Review X 3

2013

Cited alongside, same era.

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. 2013

Original

2013

Cited alongside, same era.

C. Wang, A. C. Potter, and T. Senthil, “Gapped Symmetry Preserving Surface State for the Electron Topological Insulator,” Phys. Rev. B 88

2013

Cited alongside, same era.

A. Vishwanath and T. Senthil “Physics of Three Dimensional Bosonic Topological Insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect,” Phys. Rev. X3 (2013) 1, 011016 arXiv:1209.3058 [cond-mat.str-el]

Original

2013