Speaker
Description
The gauge principle is a cornerstone of model building, yet most constructions gauge only the $SU(N)$ factors while leaving the associated $U(1)$ phase redundancies global. I take the gauge principle to its logical extreme and promote all $SU(N)$ groups to $U(N)$, proposing that the underlying symmetry of the strong and electroweak interactions is not $SU(3)_c \times SU(2)_L \times U(1)_Y$ but $U(3) \times U(2)$. Since $U(N) \cong \left[ SU(N) \times U(1) \right] / \mathbb{Z}_N$, the global structure of the group restricts the allowed representations and, combined with anomaly cancellation, turns several ad hoc features of the Standard Model into predictions: charge quantization and the observed hypercharge assignments. Consistency also requires right-handed neutrinos and an extra gauged $U(1)$, which can be identified with $B-L$, so that neutrino masses arise naturally. I will also comment on the associated $Z'$, dark matter from residual discrete symmetries, and the extension to grand unification, where flipped $SU(5)$ is recovered as $U(5)$. I will also argue that fully embracing the gauge principle opens novel avenues for model building, in particular in the flavor sector, where family symmetries are routinely introduced at the algebra level and the global structure of the group is systematically overlooked.