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The notion of symmetries has been generalized drastically in recent years. These generalized global symmetries have shown to be extremely powerful in deepening our understanding of QFT. The appearance and usage of generalized global symmetries in particle physics are yet to be explored and this talk will provide two such stories.
In the first par of the talk, I will discuss various ways of coupling the axion-Maxwell theory to a sector of topological field theory (TQFT). Contrary to common wisdom, I will show that such topological modifications can lead to interesting theoretical and observable consequences.
In the second part of the talk, I will show that the SM supplemented with an extra U(1) gauge group can possess non-invertible global symmetries and these new symmetries can protect the neutrino mass operator from being generated. An exponentially small neutrino mass can then be induced by a non-perturbative violation of non-invertible symmetry by UV monopoles.