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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 , 1910.11277
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 , 1910.14668
Original
1910
Earlier work this paper cites.
S. P. Novikov, On manifolds with free abelian fundamental group and their application , Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya 30
1966
Earlier work this paper cites.
J. Wess and B. Zumino, Consequences of anomalous Ward identities , Phys. Lett. B 37
1971
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi and I. M. Singer, Spectral asymmetry and Riemannian geometry. III , Mathematical Proceedings of the Cambridge Philosophical Society 79
1976
Earlier work this paper cites.
A. Back, P. G. O. Freund and M. Forger, New Gravitational Instantons and Universal Spin Structures , Phys. Lett. 77B
1978
Earlier work this paper cites.
S. W. Hawking and C. N. Pope, Generalized Spin Structures in Quantum Gravity , Phys. Lett. 73B
1978
Earlier work this paper cites.

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2020

Davighi, Joe, Lohitsiri, Nakarin

We discuss anomaly cancellation in $U(2)$ gauge theories in four dimensions.

For a $U(2)$ gauge theory defined with a spin structure, the vanishing of the bordism group $\Omega_5^{\text{Spin}}(BU(2))$ implies that there can be no global anomalies, in contrast to the related case of an $SU(2)$ gauge theory.
We show explicitly that the familiar $SU(2)$ global anomaly is replaced by a local anomaly when $SU(2)$ is embedded in $U(2)$.
There must be an even number of fermions with isospin $2r+1/2$, for $r\in \mathbb{Z}_{\geq 0}$, for this local anomaly to cancel.

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 , 1910.11277
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 , 1910.14668
Original
1910
Earlier work this paper cites.
S. P. Novikov, On manifolds with free abelian fundamental group and their application , Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya 30
1966
Earlier work this paper cites.
J. Wess and B. Zumino, Consequences of anomalous Ward identities , Phys. Lett. B 37
1971
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi and I. M. Singer, Spectral asymmetry and Riemannian geometry. III , Mathematical Proceedings of the Cambridge Philosophical Society 79
1976
Earlier work this paper cites.
A. Back, P. G. O. Freund and M. Forger, New Gravitational Instantons and Universal Spin Structures , Phys. Lett. 77B
1978
Earlier work this paper cites.
S. W. Hawking and C. N. Pope, Generalized Spin Structures in Quantum Gravity , Phys. Lett. 73B
1978
Earlier work this paper cites.

S. J. Avis and C. J. Isham, Generalized spin structures on four-dimensional space-times , Commun. Math. Phys. 72
1980
Cited alongside, same era.
E. Witten, An SU(2) Anomaly , Phys. Lett. 117B
1982
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.
L. Alvarez-Gaume and E. Witten, Gravitational Anomalies , Nucl. Phys. B 234
1984
Cited alongside, same era.
E. Witten, Global gravitational anomalies , Commun. Math. Phys. 100
1985
Cited alongside, same era.
J. Preskill, Gauge anomalies in an effective field theory , Annals Phys. 210
1991
Cited alongside, same era.