Abstract
We analyse global anomalies and related constraints in the Standard Model (SM) and various Beyond the Standard Model (BSM) theories. We begin by considering four distinct, but equally valid, versions of the SM, in which the gauge group is taken to be G = GSM/Γn, with GSM = SU(3) × SU(2) × U(1) and Γn isomorphic to ℤ/n where n ∈ {1, 2, 3, 6}. In addition to deriving constraints on the hypercharges of fields transforming in arbitrary representations of the SU(3) × SU(2) factor, we study the possibility of global anomalies in theories with these gauge groups by computing the bordism groups {Omega}_5^{mathrm{Spin}}(BG) using the Atiyah-Hirzebruch spectral sequence. In two cases we show that there are no global anomalies beyond the Witten anomaly, while in the other cases we show that there are no global anomalies at all, illustrating the subtle interplay between local and global anomalies. While freedom from global anomalies has been previously shown for the specific fermion content of the SM by embedding the SM in an anomaly-free SU(5) GUT, our results here remain true when the SM fermion content is extended arbitrarily. Going beyond the SM gauge groups, we show that there are no new global anomalies in extensions of the (usual) SM gauge group by U(1)m for any integer m, which correspond to phenomenologically well-motivated BSM theories featuring multiple Z′ bosons. Nor do we find any new global anomalies in various grand unified theories, including Pati-Salam and trinification models. We also consider global anomalies in a family of theories with gauge group SU(N ) × Sp(M ) × U(1), which share the phase structure of the SM for certain (N, M ). Lastly, we discuss a BSM theory in which the SM fermions are defined using a spinc structure, for example by gauging B − L. Such a theory may be extended to all orientable four-manifolds, and we find no global anomalies.
Highlights
The Standard Model (SM) has been tremendously successful in explaining all the data collected from collider physics experiments such as at the LHC, with the gauge, flavour, and Higgs sectors having been tested at the per mille, per cent, and ten per cent levels respectively [1]
In addition to deriving constraints on the hypercharges of fields transforming in arbitrary representations of the SU(3) × SU(2) factor, we study the possibility of global anomalies in theories with these gauge groups by computing the bordism groups ΩS5pin(BG) using the Atiyah-Hirzebruch spectral sequence
The computations we report in this paper build upon those of ref. [10], which used the Atiyah-Hirzebruch spectral sequence to compute ΩSd≤pi5n(BG) for a number of simple gauge groups G including SU(n), PSU(n), USp(2k), and SO(n), as well as for U(1)
Summary
The Standard Model (SM) has been tremendously successful in explaining all the data collected from collider physics experiments such as at the LHC, with the gauge, flavour, and Higgs sectors having been tested at the per mille, per cent, and ten per cent levels respectively [1]. [10] that there are no global anomalies in the SMs, by exploiting the (perhaps fortuitous) fact that the particular fermion content of the SM can be embedded in an anomaly-free grand unified theory (GUT) with G = SU(5) (which breaks down to GSM/Γ6 as we go below the GUT scale) Alternative derivations of this result can be found in refs. This is related to the more mundane fact that for the gauge groups featuring quotients by Γn=1 there are non-trivial constraints on the hypercharges of fermions depending on their representation. Ref. [14], which has subsequently appeared, confirms some of the bordism group calculations in this paper using the Adams spectral sequence
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