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The Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases.
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L. Alvarez-Gaume, S. Della Pietra and G. W. Moore, “Anomalies and Odd Dimensions,” Annals Phys. 163
1985
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2016
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2016
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Y. Tachikawa and K. Yonekura, “Gauge interactions and topological phases of matter,” PTEP 2016
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D. B. Kaplan, “A Method for simulating chiral fermions on the lattice,” Phys. Lett. B 288
1992
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Y. Shamir, “Chiral fermions from lattice boundaries,” Nucl. Phys. B 406
1993
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M. F. L. Golterman, K. Jansen and D. B. Kaplan, “Chern-Simons currents and chiral fermions on the lattice,” Phys. Lett. B 301
1993
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V. Furman and Y. Shamir, “Axial symmetries in lattice QCD with Kaplan fermions,” Nucl. Phys. B 439
1995
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D. B. Kaplan and M. Schmaltz, “Domain wall fermions and the eta invariant,” Phys. Lett. B 368
1996
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H. Neuberger, “Exactly massless quarks on the lattice,” Phys. Lett. B 417
1998
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H. Neuberger, “More about exactly massless quarks on the lattice,” Phys. Lett. B 427
1998
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E. Witten, “The ‘Parity’ Anomaly On An Unorientable Manifold,” Phys. Rev. B 94
2016
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K. Yonekura, “Dai-Freed theorem and topological phases of matter,” JHEP 1609
2016
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2016
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K. i. Okumura and H. Suzuki, “Fermion number anomaly with the fluffy mirror fermion,” PTEP 2016
2016
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2017
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2017
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2017
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Y. Hamada and H. Kawai, “Axial U(1) current in Grabowska and Kaplan’s formulation,” PTEP 2017
2017
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2017
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A. J. Niemi and G. W. Semenoff, “Axial Anomaly Induced Fermion Fractionization and Effective Gauge Theory Actions in Odd Dimensional Space-Times,” Phys. Rev. Lett. 51
2077
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