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…