Built on

C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications II , SciPost Phys. 8
Original
1905
Earlier work this paper cites.
R. Kobayashi, K. Ohmori, and Y. Tachikawa, On gapped boundaries for SPT phases beyond group cohomology , JHEP 11
Original
1905
Earlier work this paper cites.
E. Witten and K. Yonekura, Anomaly Inflow and the η \eta -Invariant , The Shoucheng Zhang Memorial Workshop Stanford, CA, USA, May 2-4, 2019, 2019. arXiv:1909.08775 [hep-th]
Original
1909
Earlier work this paper cites.
H.-C. Kim, H.-C. Tarazi, and C. Vafa, Four-dimensional 𝒩 = 𝟒 \mathbf{\mathcal{N}=4} SYM theory and the swampland , Phys. Rev. D 102
Original
1912
Earlier work this paper cites.
J.-P. Serre, Cohomologie modulo 2 2 des complexes d’Eilenberg-MacLane , Comment. Math. Helv. 27
1953
Earlier work this paper cites.
A. Borel, Sur l’homologie et la cohomologie des groupes de Lie compacts connexes , Amer. J. Math. 76
1954
Earlier work this paper cites.
R. Bott and H. Samelson, Applications of the theory of Morse to symmetric spaces , Amer. J. Math. 80
1958
Earlier work this paper cites.
D. W. Anderson, E. H. Brown, Jr., and F. P. Peterson, The structure of the Spin cobordism ring , Ann. of Math. (2) 86
1967
Earlier work this paper cites.
H. Kachi, Homotopy groups of compact Lie groups E 6 , E 7 E_{6},\,E_{7} and E 8 E_{8} , Nagoya Math. J. 32
1968
Earlier work this paper cites.
D. Quillen, The mod {\rm mod} 2 2 cohomology rings of extra-special 2 2 -groups and the spinor groups , Math. Ann. 194
1971
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I , Math. Proc. Cambridge Philos. Soc. 77
1975
Earlier work this paper cites.
M. Mimura and H. Toda, Topology of Lie groups. I, II , Translations of Mathematical Monographs, vol. 91, American Mathematical Society, Providence, RI, 1991. Translated from the 1978 Japanese edition by the authors
1978
Earlier work this paper cites.
E. Witten, An SU(2) Anomaly , Phys. Lett. B 117
1982
Earlier work this paper cites.
L. Alvarez-Gaume and P. H. Ginsparg, The Topological Meaning of Nonabelian Anomalies , Nucl. Phys. B 243
1984
Earlier work this paper cites.
L. Álvarez-Gaumé and E. Witten, Gravitational Anomalies , Nucl. Phys. B 234
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

O. Alvarez, I. M. Singer, and B. Zumino, Gravitational Anomalies and the Family’s Index Theorem , Commun. Math. Phys. 96
1984
Cited alongside, same era.
M. B. Green and J. H. Schwarz, Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory , Phys. Lett. B 149
1984
Cited alongside, same era.
J. Cheeger and J. Simons, Differential characters and geometric invariants , Geometry and topology, Lecture Notes in Math., vol. 1167, Springer, Berlin, 1985, pp. 50–80
1985
Cited alongside, same era.
R. E. Stong, Appendix: Calculation of Ω 11 Spin ( K ⁡ ( ℤ , 4 ) ) \Omega^{{\rm Spin}}_{11}(K(\mathbb{Z},4)) , Workshop on Unified String Theories (1985), World Scientific, 1986, pp. 430–437
1986
Cited alongside, same era.
P. Teichner, On the signature of four-manifolds with universal covering spin , Math. Ann. 295
1993

Then

M. Montero and C. Vafa, Cobordism Conjecture, Anomalies, and the String Lamppost Principle , JHEP 01
Original
2008
Later among the works it cites.
J. Davighi and N. Lohitsiri, Omega vs. pi, and 6d anomaly cancellation , JHEP 05
Original
2012
Later among the works it cites.
Y. Lee and Y. Tachikawa, Some comments on 6d global gauge anomalies , PTEP 2021
Original
2012
Later among the works it cites.
D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, Generalized Global Symmetries , JHEP 02
Original
2015
Later among the works it cites.
A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, Fermionic Symmetry Protected Topological Phases and Cobordisms , JHEP 12
Original

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

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2022

Global anomalies in 8d supergravity

Lee, Yasunori, Yonekura, Kazuya

Understand

We study gauge and gravitational anomalies of fermions and 2-form fields on eight-dimensional spin manifolds.

Possible global gauge anomalies are classified by spin bordism groups $\Omega^{\text{spin}}_9(BG)$ which we determine by spectral sequence techniques, and we also identify their explicit generator manifolds.
It turns out that a fermion in the adjoint representation of any simple Lie group, and a gravitino in $8d$ $\mathcal{N}=1$ supergravity theory, have anomalies.
We discuss how a 2-form field, which also appears in supergravity, produces anomalies which cancel against these fermion anomalies in a certain class of supergravity theories.

Built on

C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications II , SciPost Phys. 8
Original
1905
Earlier work this paper cites.
R. Kobayashi, K. Ohmori, and Y. Tachikawa, On gapped boundaries for SPT phases beyond group cohomology , JHEP 11
Original
1905
Earlier work this paper cites.
E. Witten and K. Yonekura, Anomaly Inflow and the η \eta -Invariant , The Shoucheng Zhang Memorial Workshop Stanford, CA, USA, May 2-4, 2019, 2019. arXiv:1909.08775 [hep-th]
Original
1909
Earlier work this paper cites.
H.-C. Kim, H.-C. Tarazi, and C. Vafa, Four-dimensional 𝒩 = 𝟒 \mathbf{\mathcal{N}=4} SYM theory and the swampland , Phys. Rev. D 102
Original
1912
Earlier work this paper cites.
J.-P. Serre, Cohomologie modulo 2 2 des complexes d’Eilenberg-MacLane , Comment. Math. Helv. 27
1953
Earlier work this paper cites.
A. Borel, Sur l’homologie et la cohomologie des groupes de Lie compacts connexes , Amer. J. Math. 76
1954
Earlier work this paper cites.
R. Bott and H. Samelson, Applications of the theory of Morse to symmetric spaces , Amer. J. Math. 80
1958
Earlier work this paper cites.
D. W. Anderson, E. H. Brown, Jr., and F. P. Peterson, The structure of the Spin cobordism ring , Ann. of Math. (2) 86
1967
Earlier work this paper cites.
H. Kachi, Homotopy groups of compact Lie groups E 6 , E 7 E_{6},\,E_{7} and E 8 E_{8} , Nagoya Math. J. 32
1968
Earlier work this paper cites.
D. Quillen, The mod {\rm mod} 2 2 cohomology rings of extra-special 2 2 -groups and the spinor groups , Math. Ann. 194
1971
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I , Math. Proc. Cambridge Philos. Soc. 77
1975
Earlier work this paper cites.
M. Mimura and H. Toda, Topology of Lie groups. I, II , Translations of Mathematical Monographs, vol. 91, American Mathematical Society, Providence, RI, 1991. Translated from the 1978 Japanese edition by the authors
1978
Earlier work this paper cites.
E. Witten, An SU(2) Anomaly , Phys. Lett. B 117
1982
Earlier work this paper cites.
L. Alvarez-Gaume and P. H. Ginsparg, The Topological Meaning of Nonabelian Anomalies , Nucl. Phys. B 243
1984
Earlier work this paper cites.
L. Álvarez-Gaumé and E. Witten, Gravitational Anomalies , Nucl. Phys. B 234
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

O. Alvarez, I. M. Singer, and B. Zumino, Gravitational Anomalies and the Family’s Index Theorem , Commun. Math. Phys. 96
1984
Cited alongside, same era.
M. B. Green and J. H. Schwarz, Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory , Phys. Lett. B 149
1984
Cited alongside, same era.
J. Cheeger and J. Simons, Differential characters and geometric invariants , Geometry and topology, Lecture Notes in Math., vol. 1167, Springer, Berlin, 1985, pp. 50–80
1985
Cited alongside, same era.
R. E. Stong, Appendix: Calculation of Ω 11 Spin ( K ⁡ ( ℤ , 4 ) ) \Omega^{{\rm Spin}}_{11}(K(\mathbb{Z},4)) , Workshop on Unified String Theories (1985), World Scientific, 1986, pp. 430–437
1986
Cited alongside, same era.
P. Teichner, On the signature of four-manifolds with universal covering spin , Math. Ann. 295
1993

Then

M. Montero and C. Vafa, Cobordism Conjecture, Anomalies, and the String Lamppost Principle , JHEP 01
Original
2008
Later among the works it cites.
J. Davighi and N. Lohitsiri, Omega vs. pi, and 6d anomaly cancellation , JHEP 05
Original
2012
Later among the works it cites.
Y. Lee and Y. Tachikawa, Some comments on 6d global gauge anomalies , PTEP 2021
Original
2012
Later among the works it cites.
D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, Generalized Global Symmetries , JHEP 02
Original
2015
Later among the works it cites.
A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, Fermionic Symmetry Protected Topological Phases and Cobordisms , JHEP 12
Original

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

S. Chaudhuri, G. Hockney, and J. D. Lykken, Maximally supersymmetric string theories in D < < 10 , Phys. Rev. Lett. 75

1995

Cited alongside, same era.

D. R. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds. 1 , Nucl. Phys. B 473

1996

Cited alongside, same era.

C. Vafa, Evidence for F theory , Nucl. Phys. B 469

1996

Cited alongside, same era.

D. S. Freed and M. J. Hopkins, On Ramond-Ramond fields and K theory , JHEP 05

2000

Cited alongside, same era.

J. F. Davis and P. Kirk, Lecture notes in algebraic topology , Graduate Studies in Mathematics, vol. 35, American Mathematical Society, Providence, RI, 2001

2001

Cited alongside, same era.

J. McCleary, A user’s guide to spectral sequences , 2nd ed., Cambridge Studies in Advanced Mathematics, vol. 58, Cambridge University Press, Cambridge, 2001

2001

Cited alongside, same era.

C.-T. Hsieh, Y. Tachikawa, and K. Yonekura, Anomaly inflow and p p -form gauge theories , arXiv:2003.11550 [hep-th]

Original

2003

Cited alongside, same era.

2015