Global anomalies in the Standard Model(s) and Beyond

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 $G=G_{\text{SM}}/{\Gamma }_n$, with $G_{\text{SM}}=SU(3)\times SU(2)\times U(1)$ and ${\Gamma }_n$ isomorphic to $\mathbb{Z}/n$ where $n\in \left\{1,2,3,6\right\}$. In addition to deriving constraints on the hypercharges of fields transforming in arbitrary representations of the $SU(3)\times SU(2)$ factor, we study the possibility of global anomalies in theories with these gauge groups by computing the bordism groups ${\Omega }_5^{\text{Spin}}(BG)$ 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 $Z^{\prime }$ 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 $SU(N)\times Sp(M)\times U(1)$, which share the phase structure of the SM for certain $(N,M)$.

arXiv comment59 pages, 11 figures. Section on the SO(18) GUT removed; paragraph added concerning non-nullbordant spacetimes; minor corrections and references updated

References in corpus (18)

• The Physics of Heavy Z' Gauge Bosons
• Fermion Path Integrals And Topological Phases
• Five-Brane Effective Action In M-Theory
• The "Parity" Anomaly On An Unorientable Manifold
• Eta-Invariants and Determinant Lines
• Dai-Freed anomalies in particle physics
• Setting the quantum integrand of M-theory
• A New SU(2) Anomaly
• Higher Anomalies, Higher Symmetries, and Cobordisms I: Classification of Higher-Symmetry-Protected Topological States and Their Boundary Fermionic/Bosonic Anomalies via a Generalized Cobordism Theory
• Line Operators in the Standard Model
• General solution to the U(1) anomaly equations
• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
• Dai-Freed theorem and topological phases of matter
• Anomaly-Free Models for Flavour Anomalies
• A Non-Perturbative Definition of the Standard Models
• Anomaly interplay in $U(2)$ gauge theories
• Hamiltonian anomalies from extended field theories
• If the Weak Were Strong and the Strong Were Weak

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