Built on

P.-S. Hsin and A. Turzillo, Symmetry-enriched quantum spin liquids in (3 + 1) d d , JHEP 09
Original
1904
Earlier work this paper cites.
C.-T. Hsieh, Y. Tachikawa and K. Yonekura, Anomaly of the Electromagnetic Duality of Maxwell Theory , Phys. Rev. Lett. 123
Original
1905
Earlier work this paper cites.
E. Witten and K. Yonekura, Anomaly Inflow and the η \eta -Invariant , 1909.08775
Original
1909
Earlier work this paper cites.
J. Davighi, B. Gripaios and N. Lohitsiri, Global anomalies in the Standard Model(s) and Beyond , JHEP 07
Original
1910
Earlier work this paper cites.
Z. Wan and J. Wang, Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms , JHEP 07
Original
1910
Earlier work this paper cites.
C. Córdova, K. Ohmori, S.-H. Shao and F. Yan, Decorated ℤ 2 \mathbb{Z}_{2} symmetry defects and their time-reversal anomalies , Phys. Rev. D 102
Original
1910
Earlier work this paper cites.
I. Hason, Z. Komargodski and R. Thorngren, Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism , SciPost Phys. 8
Original
1910
Earlier work this paper cites.
J. Ang, K. Roumpedakis and S. Seifnashri, Line Operators of Gauge Theories on Non-Spin Manifolds , JHEP 04
Original
1911
Earlier work this paper cites.
W.-t. Wu, Classes caractéristiques et i i -carrés d’une variété , C. R. Acad. Sci., Paris 230
1950
Earlier work this paper cites.
J.-P. Serre, Homologie singuliere des espaces fibres , Annals of Mathematics 54
1951
Earlier work this paper cites.
J.-P. Serre, Cohomologie modulo 2 des complexes d’eilenberg-maclane , Commentarii Mathematici Helvetici 27
1953
Earlier work this paper cites.
J. F. Adams, On the structure and applications of the steenrod algebra , Commentarii Mathematici Helvetici 32
1958
Earlier work this paper cites.
C. T. C. Wall, Determination of the cobordism ring , Annals of Mathematics 72
1960
Earlier work this paper cites.
M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces , in Proceedings of Symposia in Pure Mathematics (C. B. Allendoerfer, ed.), vol. 3, pp. 7–38, American Mathematical Society, 1961
1961
Earlier work this paper cites.
A. L. Liulevicius, The cohomology of a subalgebra of the Steenrod algebra , Trans. Amer. Math. Soc. 104
1962
Earlier work this paper cites.
G. Segal, Classifying spaces and spectral sequences , Publications Mathématiques de l’Institut des Hautes Scientifiques 34
1968
Earlier work this paper cites.
M. Atiyah, V. Patodi and I. Singer, Spectral asymmetry and Riemannian Geometry 1 , Math. Proc. Cambridge Phil. Soc. 77
1975
Earlier work this paper cites.
M. Atiyah, V. Patodi and I. Singer, Spectral asymmetry and Riemannian geometry 2 , Math. Proc. Cambridge Phil. Soc. 78
1976
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi and I. M. Singer, Spectral asymmetry and Riemannian geometry. III , Math. Proc. Cambridge Phil. Soc. 79
1976
Earlier work this paper cites.
Springer, 1982
K. S. Brown, Cohomology of Groups · 1982
Earlier work this paper cites.
E. Witten, Global aspects of current algebra , Nuclear Physics B 223
1983
Earlier work this paper cites.
S. Elitzur and V. Nair, Nonperturbative Anomalies in Higher Dimensions , Nucl. Phys. B 243
1984
Earlier work this paper cites.
E. Witten, Global Gravitational Anomalies , Commun. Math. Phys. 100
1985
Earlier work this paper cites.
A. Bahri and P. Gilkey, The eta invariant, pinc bordism, and equivariant spinc bordism for cyclic 2-groups , Pacific journal of mathematics 128
1987
Earlier work this paper cites.
P. Teichner, On the signature of four-manifolds with universal covering spin , Mathematische Annalen 295
1993
Earlier work this paper cites.
X.-z. Dai and D. S. Freed, eta invariants and determinant lines , J. Math. Phys. 35
1994
Earlier work this paper cites.

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2023

Toric 2-group anomalies via cobordism

Davighi, Joe, Lohitsiri, Nakarin

Understand

2-group symmetries arise in physics when a 0-form symmetry $G^{[0]}$ and a 1-form symmetry $H^{[1]}$ intertwine, forming a generalised group-like structure.

Specialising to the case where both $G^{[0]}$ and $H^{[1]}$ are compact, connected, abelian groups (i.e.
tori), we analyse anomalies in such `toric 2-group symmetries' using the cobordism classification.
As a warm up example, we use cobordism to study various 't Hooft anomalies (and the phases to which they are dual) in Maxwell theory defined on non-spin manifolds.

Built on

P.-S. Hsin and A. Turzillo, Symmetry-enriched quantum spin liquids in (3 + 1) d d , JHEP 09
Original
1904
Earlier work this paper cites.
C.-T. Hsieh, Y. Tachikawa and K. Yonekura, Anomaly of the Electromagnetic Duality of Maxwell Theory , Phys. Rev. Lett. 123
Original
1905
Earlier work this paper cites.
E. Witten and K. Yonekura, Anomaly Inflow and the η \eta -Invariant , 1909.08775
Original
1909
Earlier work this paper cites.
J. Davighi, B. Gripaios and N. Lohitsiri, Global anomalies in the Standard Model(s) and Beyond , JHEP 07
Original
1910
Earlier work this paper cites.
Z. Wan and J. Wang, Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms , JHEP 07
Original
1910
Earlier work this paper cites.
C. Córdova, K. Ohmori, S.-H. Shao and F. Yan, Decorated ℤ 2 \mathbb{Z}_{2} symmetry defects and their time-reversal anomalies , Phys. Rev. D 102
Original
1910
Earlier work this paper cites.
I. Hason, Z. Komargodski and R. Thorngren, Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism , SciPost Phys. 8
Original
1910
Earlier work this paper cites.
J. Ang, K. Roumpedakis and S. Seifnashri, Line Operators of Gauge Theories on Non-Spin Manifolds , JHEP 04
Original
1911
Earlier work this paper cites.
W.-t. Wu, Classes caractéristiques et i i -carrés d’une variété , C. R. Acad. Sci., Paris 230
1950
Earlier work this paper cites.
J.-P. Serre, Homologie singuliere des espaces fibres , Annals of Mathematics 54
1951
Earlier work this paper cites.
J.-P. Serre, Cohomologie modulo 2 des complexes d’eilenberg-maclane , Commentarii Mathematici Helvetici 27
1953
Earlier work this paper cites.
J. F. Adams, On the structure and applications of the steenrod algebra , Commentarii Mathematici Helvetici 32
1958
Earlier work this paper cites.
C. T. C. Wall, Determination of the cobordism ring , Annals of Mathematics 72
1960
Earlier work this paper cites.
M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces , in Proceedings of Symposia in Pure Mathematics (C. B. Allendoerfer, ed.), vol. 3, pp. 7–38, American Mathematical Society, 1961
1961
Earlier work this paper cites.
A. L. Liulevicius, The cohomology of a subalgebra of the Steenrod algebra , Trans. Amer. Math. Soc. 104
1962
Earlier work this paper cites.
G. Segal, Classifying spaces and spectral sequences , Publications Mathématiques de l’Institut des Hautes Scientifiques 34
1968
Earlier work this paper cites.
M. Atiyah, V. Patodi and I. Singer, Spectral asymmetry and Riemannian Geometry 1 , Math. Proc. Cambridge Phil. Soc. 77
1975
Earlier work this paper cites.
M. Atiyah, V. Patodi and I. Singer, Spectral asymmetry and Riemannian geometry 2 , Math. Proc. Cambridge Phil. Soc. 78
1976
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi and I. M. Singer, Spectral asymmetry and Riemannian geometry. III , Math. Proc. Cambridge Phil. Soc. 79
1976
Earlier work this paper cites.
Springer, 1982
K. S. Brown, Cohomology of Groups · 1982
Earlier work this paper cites.
E. Witten, Global aspects of current algebra , Nuclear Physics B 223
1983
Earlier work this paper cites.
S. Elitzur and V. Nair, Nonperturbative Anomalies in Higher Dimensions , Nucl. Phys. B 243
1984
Earlier work this paper cites.
E. Witten, Global Gravitational Anomalies , Commun. Math. Phys. 100
1985
Earlier work this paper cites.
A. Bahri and P. Gilkey, The eta invariant, pinc bordism, and equivariant spinc bordism for cyclic 2-groups , Pacific journal of mathematics 128
1987
Earlier work this paper cites.
P. Teichner, On the signature of four-manifolds with universal covering spin , Mathematische Annalen 295
1993
Earlier work this paper cites.
X.-z. Dai and D. S. Freed, eta invariants and determinant lines , J. Math. Phys. 35
1994
Earlier work this paper cites.

Similar

Cambridge Studies in Advanced Mathematics. Cambridge University Press, 2 ed., 2000, 10.1017/CBO9780511626289
J. McCleary, A User’s Guide to Spectral Sequences · 2000
Cited alongside, same era.
J. Davighi and N. Lohitsiri, Anomaly interplay in U ⁡ ( 2 ) U(2) gauge theories , JHEP 05
Original
2001
Cited alongside, same era.
University of California, Riverside, 2006
T. K. Bartels, Higher gauge theory: 2-bundles · 2006
Cited alongside, same era.
D. S. Freed and G. W. Moore, Setting the quantum integrand of M-theory , Commun. Math. Phys. 263
2006
Cited alongside, same era.
P.-S. Hsin and H. T. Lam, Discrete theta angles, symmetries and anomalies , SciPost Phys. 10
Original
2007
Cited alongside, same era.