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Description
Over the past decade, field theorists have developed a novel framework for thinking about global symmetries which has enormously generalized our understanding thereof. Recently my collaborators and I have established positively that past being a useful formal tool, such generalized symmetries are indeed present in models that we care about as particle physicists - and furthermore understanding them can lead to new insights into these models.
After discussing the generalized symmetries of the Standard Model, we will go Beyond and show that the identification of a non-invertible symmetry of $Z'$ models of $L_\mu - L_\tau$ reveals the existence of simple UV completions thereof where the scale of neutrino masses is exponentially suppressed from that of charged leptons. Next we will uncover a subtler non-invertible symmetry in horizontal gauge theories of the quark sector which exists by virtue of the SM having the same numbers of colors and generations, and points to a massless down quarks solution to strong CP in color-flavor unification.
