Built on

S. Monnier, “A Modern Point Of View On Anomalies,” arXiv:1903.02828
Original
1903
Earlier work this paper cites.
A. Dabholkar, D. Jain, and A. Rudra, “APS η \eta -Invariant, Path Integrals, and Mock Modularity,” arXiv:1905.05207
Original
1905
Earlier work this paper cites.
C. T. Hsieh, Y. Tachikawa and K. Yonekura, “On the Anomaly of the Electromagnetic Duality of the Maxwell Theory,” arXiv:1905.08943 [hep-th]
Original
1905
Earlier work this paper cites.
I. Fialkovsky, M. Kurkov and D. Vassilevich, “Quantum Dirac Fermions in a Half-space and Their Interaction with an Electromagnetic Field,” Phys. Rev. D 100
Original
1906
Earlier work this paper cites.
D. Stanford and E. Witten, “JT Gravity And The Ensembles Of Random Matrix Theory,” arXiv:1907.03363 [hep-th]
Original
1907
Earlier work this paper cites.
D. S. Freed and M. J. Hopkins, “M-Theory Anomaly Cancellation,” arXiv:1908.09916 [hep-th]
Original
1908
Earlier work this paper cites.
J. Kaidi, J. Parro-Martinez, and Y. Tachikawa, “GSO Projections Via SPT Phases,” arXiv:1908.04805 [hep-th]
Original
1908
Earlier work this paper cites.
M. F. Atiyah and I. M. Singer, “The Index Of Elliptic Operators, I,” Ann. Math. 87
1968
Earlier work this paper cites.
S. L. Adler, “Axial Vector Vertex in Spinor Electrodynamics,” Phys. Rev. 177
1969
Earlier work this paper cites.
J. S. Bell and R. Jackiw, “A PCAC puzzle: π 0 → γ γ \pi^{0}\to\gamma\gamma in the σ \sigma Model,” Nuovo Cim. A 60
1969
Earlier work this paper cites.
H. Georgi and S. L. Glashow, “Unity of All Elementary Particle Forces,” Phys. Rev. Lett. 32
1974
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi and I. M. Singer, “Spectral Asymmetry and Riemannian Geometry 1,” Math. Proc. Cambridge Phil. Soc. 77
1975
Earlier work this paper cites.
F. Gliozzi, D. Olive, and J. Scherk, “Supersymmetry, Supergravity Theories, and the Dual Spinor Model,” Nucl. Phys. B122
1977
Earlier work this paper cites.
M. Hortacsu, K. D. Rothe and B. Schroer, “Zero Energy Eigenstates for the Dirac Boundary Problem,” Nucl. Phys. B 171
1980
Earlier work this paper cites.
E. Witten, “An SU(2) Anomaly,” Phys. Lett. 117B
1982
Earlier work this paper cites.
R. Stora, “Algebraic Structure And Topological Origin of Anomalies,” in Progress in Gauge Field Theory
1984
Earlier work this paper cites.
N. Redlich, “Gauge Noninvariance and Parity Violation of Three-Dimensional Fermions,” Phys. Rev. Lett. 52
1984
Earlier work this paper cites.
M. F. Atiyah and I. M. Singer, “Dirac Operators Coupled to Vector Potentials,” Proc. Nat. Acad. Sci. 81
1984
Earlier work this paper cites.

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1985
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Later among the works it cites.
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2019

Anomaly Inflow and the $\eta$-Invariant

Witten, Edward, Yonekura, Kazuya

Understand

Perturbative fermion anomalies in spacetime dimension $d$ have a well-known relation to Chern-Simons functions in dimension $D=d+1$.

This relationship is manifested in a beautiful way in "anomaly inflow" from the bulk of a system to its boundary.
Along with perturbative anomalies, fermions also have global or nonperturbative anomalies, which can be incorporated by using the $\eta$-invariant of Atiyah, Patodi, and Singer instead of the Chern-Simons function.
Here we give a nonperturbative description of anomaly inflow, involving the $\eta$-invariant.

Built on

S. Monnier, “A Modern Point Of View On Anomalies,” arXiv:1903.02828
Original
1903
Earlier work this paper cites.
A. Dabholkar, D. Jain, and A. Rudra, “APS η \eta -Invariant, Path Integrals, and Mock Modularity,” arXiv:1905.05207
Original
1905
Earlier work this paper cites.
C. T. Hsieh, Y. Tachikawa and K. Yonekura, “On the Anomaly of the Electromagnetic Duality of the Maxwell Theory,” arXiv:1905.08943 [hep-th]
Original
1905
Earlier work this paper cites.
I. Fialkovsky, M. Kurkov and D. Vassilevich, “Quantum Dirac Fermions in a Half-space and Their Interaction with an Electromagnetic Field,” Phys. Rev. D 100
Original
1906
Earlier work this paper cites.
D. Stanford and E. Witten, “JT Gravity And The Ensembles Of Random Matrix Theory,” arXiv:1907.03363 [hep-th]
Original
1907
Earlier work this paper cites.
D. S. Freed and M. J. Hopkins, “M-Theory Anomaly Cancellation,” arXiv:1908.09916 [hep-th]
Original
1908
Earlier work this paper cites.
J. Kaidi, J. Parro-Martinez, and Y. Tachikawa, “GSO Projections Via SPT Phases,” arXiv:1908.04805 [hep-th]
Original
1908
Earlier work this paper cites.
M. F. Atiyah and I. M. Singer, “The Index Of Elliptic Operators, I,” Ann. Math. 87
1968
Earlier work this paper cites.
S. L. Adler, “Axial Vector Vertex in Spinor Electrodynamics,” Phys. Rev. 177
1969
Earlier work this paper cites.
J. S. Bell and R. Jackiw, “A PCAC puzzle: π 0 → γ γ \pi^{0}\to\gamma\gamma in the σ \sigma Model,” Nuovo Cim. A 60
1969
Earlier work this paper cites.
H. Georgi and S. L. Glashow, “Unity of All Elementary Particle Forces,” Phys. Rev. Lett. 32
1974
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi and I. M. Singer, “Spectral Asymmetry and Riemannian Geometry 1,” Math. Proc. Cambridge Phil. Soc. 77
1975
Earlier work this paper cites.
F. Gliozzi, D. Olive, and J. Scherk, “Supersymmetry, Supergravity Theories, and the Dual Spinor Model,” Nucl. Phys. B122
1977
Earlier work this paper cites.
M. Hortacsu, K. D. Rothe and B. Schroer, “Zero Energy Eigenstates for the Dirac Boundary Problem,” Nucl. Phys. B 171
1980
Earlier work this paper cites.
E. Witten, “An SU(2) Anomaly,” Phys. Lett. 117B
1982
Earlier work this paper cites.
R. Stora, “Algebraic Structure And Topological Origin of Anomalies,” in Progress in Gauge Field Theory
1984
Earlier work this paper cites.
N. Redlich, “Gauge Noninvariance and Parity Violation of Three-Dimensional Fermions,” Phys. Rev. Lett. 52
1984
Earlier work this paper cites.
M. F. Atiyah and I. M. Singer, “Dirac Operators Coupled to Vector Potentials,” Proc. Nat. Acad. Sci. 81
1984
Earlier work this paper cites.

Similar

R. Jackiw, “Topological Investigations Of Quantized Gauge Theories,” in B. S. DeWitt et. al., eds., Relativity, Groups, and Topology,II
1985
Cited alongside, same era.
B. Zumino, “Chiral Anomalies In Differential Geometry,” in B. S. DeWitt et. al., eds., Relativity, Groups, and Topology,II
1985
Cited alongside, same era.
C. G. Callan, Jr., and J. A. Harvey, “Anomalies And Fermion Zero-Modes On Strings And Domain Walls,” Nucl. Phys. B250
1985
Cited alongside, same era.
E. Witten, “Global Gravitational Anomalies,” Commun. Math. Phys. 100
1985
Cited alongside, same era.
L. Alvarez-Gaume, S. Della Pietra and G. W. Moore, “Anomalies and Odd Dimensions,” Annals Phys. 163
1985
Cited alongside, same era.