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We argue that the charge fractionalization in quarks has a hidden topological character related to a broken symmetry between integer-charged bare quarks and leptons. The mechanism is a tunneling process occurring in time between standard field configurations of a pure gauge form with different topological winding numbers associated with integer-charged bare quarks in the far past and future. This transition, which nonperturbatively normalizes local bare charges with a universal accumulated value, corresponds to a specific topologically nontrivial configuration of the weak gauge fields in Euclidean spacetime. The outcome is an effective topological charge equal to the ratio between baryon number and the number of fermion generations associated with baryonic matter. The observed conservation of baryon number is then related to the conservation of this bookkeeping charge on quarks. Baryon number violation may only arise through topological effects as in decays induced by electroweak instantons. However, stability of a free proton is expected.

The standard electroweak model with Dirac neutrinos is extended by way of the principles of electroweak quark–lepton symmetry and weak topological-charge confinement to account for quark–lepton charge relations which, if not accidental, are indicative of charge structures. A mixing in quarks and leptons of underlying integer local charges with integer weak topological charges associated with an additive group Z₃, fixed by the anomaly cancellation requirement, is discussed. It is found that the electroweak difference between topological quarks and leptons is the nonequivalence between the topological vacua of their weak field configurations, produced by a four-instanton which carries the topological charge, induces the universal fractional piece of charge distinguishing quarks from leptons, and breaks the underlying symmetry. The constituent quarks of the standard model appear as coming from topological quarks, via the weak four-instanton event. Dual transitions occur for leptons. It is shown that several other fundamental problems left open in the standard electroweak model with Dirac neutrinos are solved: the one-to-one correspondence between quark and lepton flavors, the existence of three generations, the conservation and ungauging of B-L, the electric charge quantization, and the confinement of fractional electric charges.

By considering a general Abelian chiral gauge theory, we investigate the behavior of anomalous Ward–Takahashi (WT) identities concerning their prediction for the usual relationship between the vertex and two-point fermion functions. Using gauge anomaly vanishing results, we show that the usual (in the nonanomalous case) WT identity connecting the vertex and two-point fermion 1PI functions is modified for Abelian chiral gauge theories. The modification, however, implies a relation between fermion and charge renormalization constants that can be important in a future study of renormalization of such theories.

Inspired by recent studies of high-scale decay constant or flavorful QCD axions, we review and clarify their existence in effective string models with anomalous U(1) gauge groups. We find that such models, when coupled to charged scalars getting vacuum expectation values, always have one light axion, whose mass can only come from nonperturbative effects. If the main nonperturbative effect is from QCD, then it becomes a Peccei–Quinn axion candidate for solving the strong CP problem. We then study simple models with universal Green–Schwarz mechanism and only one charged scalar field: in the minimal gaugino condensation case the axion mass is tied to the supersymmetry breaking scale and cannot be light enough, but slightly refined models maintain a massless axion all the way down to the QCD scale. Both kinds of models can be extended to yield intermediate scale axion decay constants. Finally, we gauge flavorful axion models under an anomalous U(1) and discuss the axion couplings which arise.