Anomaly Cancellation in the Metric Bundle Pati-Salam Theory

Paper 4 of 5 in the Metric Bundle Programme. We verify anomaly cancellation for the Pati-Salam gauge theory \SU(4) × \SU(2)_L × \SU(2)_R that emerges from the metric bundle Y^{14} = \Met(X^4). The fermion content derived in earlier work---the \mathbf{16}-plet of \Spin(10) ⊃ \Spin(6) × \Spin(4), decomposing as (\mathbf{4}, \mathbf{2}, \mathbf{1}) ⊕ (\bar{\mathbf{4}}, \mathbf{1}, \mathbf{2})---is shown to be free of all gauge anomalies. The purely cubic \SU(4)^3 anomaly vanishes because \mathbf{4} ⊕ \bar{\mathbf{4}} is a real representation; all \SU(2)^3 anomalies vanish because the symmetric d-tensor of \SU(2) is identically zero; and all mixed gauge-gravitational anomalies cancel because every gauge factor is non-abelian with traceless generators. The Witten \SU(2) global anomaly is absent because each \SU(2) factor sees four Weyl doublets (an even number), a consequence of the Pati-Salam unification of leptons with quarks as the fourth colour. After Pati-Salam breaking to \SU(3)_c × \SU(2)_L × \U(1)_Y, all six Standard Model anomaly conditions are verified, including the cubic \U(1)_Y^3 and the mixed \U(1)_Y-gravitational anomaly. Part of a five-paper series deriving the Pati-Salam gauge group, fermion content, gauge dynamics, anomaly cancellation, and the three-generation structure from the geometry of the metric bundle Y14 = Met(X4).