Built on

Y. Hidaka, Y. Hirono, M. Nitta, Y. Tanizaki, and R. Yokokura, Topological order in the color-flavor locked phase of a ( 3+1 )-dimensional U(N) gauge-Higgs system , Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
A. Karasik and Z. Komargodski, The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade , JHEP 05
Original
1904
Earlier work this paper cites.
C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications I , SciPost Phys. 8
Original
1905
Earlier work this paper cites.
E. Witten and K. Yonekura, Anomaly Inflow and the η \eta -Invariant , The Shoucheng Zhang Memorial Workshop, 9 2019. arXiv:1909.08775 [hep-th]
Original
1909
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. II , Math. Proc. Cambridge Phil. Soc. 78
1975
Earlier work this paper cites.
R. Jackiw and C. Rebbi, Solitons with fermion number 1 / 2 1/2 , Physical Review D 13
1976
Earlier work this paper cites.
K. Fujikawa, Path Integral Measure for Gauge Invariant Fermion Theories , Phys. Rev. Lett. 42
1979
Earlier work this paper cites.
J. Goldstone and F. Wilczek, Fractional Quantum Numbers on Solitons , Phys. Rev. Lett. 47
1981
Earlier work this paper cites.
M. V. Berry, Quantal phase factors accompanying adiabatic changes , Proc. Roy. Soc. Lond. A 392
1984
Earlier work this paper cites.
C. G. Callan Jr and J. A. Harvey, Anomalies and fermion zero modes on strings and domain walls , Nuclear Physics B 250
1985
Earlier work this paper cites.
D. Quillen, Superconnections and the chern character , Topology 24
1985
Earlier work this paper cites.
N. Berline, E. Getzler, and M. Vergne, Heat kernels and dirac operators , Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Springer-Verlag, 1992. https://books.google.com/books?id=vRc-QgAACAAJ
1992
Earlier work this paper cites.
C. Kennedy and A. Wilkins, Ramond-Ramond couplings on Brane - anti-Brane systems , Phys. Lett. B 464
1999
Earlier work this paper cites.
A. G. Abanov and P. B. Wiegmann, Theta terms in nonlinear sigma models , Nucl. Phys. B 570
2000
Earlier work this paper cites.
M. Alishahiha, H. Ita, and Y. Oz, On superconnections and the tachyon effective action , Phys. Lett. B 503
2001
Earlier work this paper cites.
H. Fukaya, M. Furuta, S. Matsuo, T. Onogi, S. Yamaguchi, and M. Yamashita, A physicist-friendly reformulation of the Atiyah-Patodi-Singer index and its mathematical justification , PoS LATTICE2019
Original
2001
Earlier work this paper cites.
P. Kraus and F. Larsen, Boundary string field theory of the D anti-D system , Phys. Rev. D 63
2001
Earlier work this paper cites.

Similar

A. Kapustin and L. Spodyneiko, Higher-dimensional generalizations of Berry curvature , Phys. Rev. B 101
Original
2001
Cited alongside, same era.
T. Takayanagi, S. Terashima, and T. Uesugi, Brane - anti-brane action from boundary string field theory , JHEP 03
2001
Cited alongside, same era.
P. Gorantla and H. T. Lam, Interface junctions in QCD 4 , SciPost Phys. 10
Original
2004
Cited alongside, same era.
P.-S. Hsin, A. Kapustin, and R. Thorngren, Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena , arXiv:2004.10758 [cond-mat.str-el]
Original
2004
Cited alongside, same era.
A. Sharon, Global Aspects of Spaces of Vacua , JHEP 11
Original

Then

A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, Fermionic Symmetry Protected Topological Phases and Cobordisms , JHEP 12
Original
2015
Later among the works it cites.
R. Thorngren, Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in 4d , JHEP 02
Original
2015
Later among the works it cites.
K. Yonekura, Dai-Freed theorem and topological phases of matter , JHEP 09
Original
2016
Later among the works it cites.
H. Fukaya, T. Onogi, and S. Yamaguchi, Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator , Phys. Rev. D 96
Original
2017
Later among the works it cites.
D. Gaiotto, A. Kapustin, Z. Komargodski, and N. Seiberg, Theta, Time Reversal, and Temperature , JHEP 05

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2022

Higher Berry Phase of Fermions and Index Theorem

Choi, Yichul, Ohmori, Kantaro

Understand

When a quantum field theory is trivially gapped, its infrared fixed point is an invertible field theory.

The partition function of the invertible field theory records the response to various background fields in the long-distance limit.
The set of background fields can include spacetime-dependent coupling constants, in which case we call the corresponding invertible theory a parameterized invertible field theory.
We study such parameterized invertible field theories arising from free Dirac fermions with spacetime-dependent mass parameters using the Atiyah-Patodi-Singer index theorem for superconnections.

Built on

Y. Hidaka, Y. Hirono, M. Nitta, Y. Tanizaki, and R. Yokokura, Topological order in the color-flavor locked phase of a ( 3+1 )-dimensional U(N) gauge-Higgs system , Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
A. Karasik and Z. Komargodski, The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade , JHEP 05
Original
1904
Earlier work this paper cites.
C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications I , SciPost Phys. 8
Original
1905
Earlier work this paper cites.
E. Witten and K. Yonekura, Anomaly Inflow and the η \eta -Invariant , The Shoucheng Zhang Memorial Workshop, 9 2019. arXiv:1909.08775 [hep-th]
Original
1909
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. II , Math. Proc. Cambridge Phil. Soc. 78
1975
Earlier work this paper cites.
R. Jackiw and C. Rebbi, Solitons with fermion number 1 / 2 1/2 , Physical Review D 13
1976
Earlier work this paper cites.
K. Fujikawa, Path Integral Measure for Gauge Invariant Fermion Theories , Phys. Rev. Lett. 42
1979
Earlier work this paper cites.
J. Goldstone and F. Wilczek, Fractional Quantum Numbers on Solitons , Phys. Rev. Lett. 47
1981
Earlier work this paper cites.
M. V. Berry, Quantal phase factors accompanying adiabatic changes , Proc. Roy. Soc. Lond. A 392
1984
Earlier work this paper cites.
C. G. Callan Jr and J. A. Harvey, Anomalies and fermion zero modes on strings and domain walls , Nuclear Physics B 250
1985
Earlier work this paper cites.
D. Quillen, Superconnections and the chern character , Topology 24
1985
Earlier work this paper cites.
N. Berline, E. Getzler, and M. Vergne, Heat kernels and dirac operators , Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Springer-Verlag, 1992. https://books.google.com/books?id=vRc-QgAACAAJ
1992
Earlier work this paper cites.
C. Kennedy and A. Wilkins, Ramond-Ramond couplings on Brane - anti-Brane systems , Phys. Lett. B 464
1999
Earlier work this paper cites.
A. G. Abanov and P. B. Wiegmann, Theta terms in nonlinear sigma models , Nucl. Phys. B 570
2000
Earlier work this paper cites.
M. Alishahiha, H. Ita, and Y. Oz, On superconnections and the tachyon effective action , Phys. Lett. B 503
2001
Earlier work this paper cites.
H. Fukaya, M. Furuta, S. Matsuo, T. Onogi, S. Yamaguchi, and M. Yamashita, A physicist-friendly reformulation of the Atiyah-Patodi-Singer index and its mathematical justification , PoS LATTICE2019
Original
2001
Earlier work this paper cites.
P. Kraus and F. Larsen, Boundary string field theory of the D anti-D system , Phys. Rev. D 63
2001
Earlier work this paper cites.

Similar

A. Kapustin and L. Spodyneiko, Higher-dimensional generalizations of Berry curvature , Phys. Rev. B 101
Original
2001
Cited alongside, same era.
T. Takayanagi, S. Terashima, and T. Uesugi, Brane - anti-brane action from boundary string field theory , JHEP 03
2001
Cited alongside, same era.
P. Gorantla and H. T. Lam, Interface junctions in QCD 4 , SciPost Phys. 10
Original
2004
Cited alongside, same era.
P.-S. Hsin, A. Kapustin, and R. Thorngren, Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena , arXiv:2004.10758 [cond-mat.str-el]
Original
2004
Cited alongside, same era.
A. Sharon, Global Aspects of Spaces of Vacua , JHEP 11
Original

Then

A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, Fermionic Symmetry Protected Topological Phases and Cobordisms , JHEP 12
Original
2015
Later among the works it cites.
R. Thorngren, Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in 4d , JHEP 02
Original
2015
Later among the works it cites.
K. Yonekura, Dai-Freed theorem and topological phases of matter , JHEP 09
Original
2016
Later among the works it cites.
H. Fukaya, T. Onogi, and S. Yamaguchi, Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator , Phys. Rev. D 96
Original
2017
Later among the works it cites.
D. Gaiotto, A. Kapustin, Z. Komargodski, and N. Seiberg, Theta, Time Reversal, and Temperature , JHEP 05

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2004

Cited alongside, same era.

T. Sulejmanpasic, Y. Tanizaki, and M. Ünsal, Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls , JHEP 06

Original

2004

Cited alongside, same era.

A. Angelescu and P. Huang, Integrating Out New Fermions at One Loop , JHEP 01

Original

2006

Cited alongside, same era.

S. A. R. Ellis, J. Quevillon, P. N. H. Vuong, T. You, and Z. Zhang, The Fermionic Universal One-Loop Effective Action , JHEP 11

Original

2006

Cited alongside, same era.

M. Ünsal, Strongly coupled QFT dynamics via TQFT coupling , JHEP 11

Original

2007

Cited alongside, same era.

M. Honda and Y. Tanizaki, Topological aspects of 4D Abelian lattice gauge theories with the θ \theta parameter , JHEP 12

Original

2009

Cited alongside, same era.

A. Kitaev, Periodic table for topological insulators and superconductors , AIP Conf. Proc. 1134

Original

2009

Cited alongside, same era.

A. Kitaev, On the classification of short-range entangled states , 2013. http://scgp.stonybrook.edu/video_portal/video.php?id=2010 . Talk at Simons Center

2010

Cited alongside, same era.

Original

2017

Later among the works it cites.

Y. Kikuchi and Y. Tanizaki, Global inconsistency, ’t Hooft anomaly, and level crossing in quantum mechanics , PTEP 2017

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2017

Later among the works it cites.

Y. Tanizaki and Y. Kikuchi, Vacuum structure of bifundamental gauge theories at finite topological angles , JHEP 06

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2017