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We propose a theoretical formulation of protected edge modes in the languageof quantum field theories based on the contemporary understanding of therenormalization group. We use bulk and boundary renormalization arguments whichhave never captured enough attention in condensed matter physics and relatedfields. We revisit various exotic bulk and boundary phenomena in contemporaryphysics, and one can see the conciseness of our formulations. Moreover, in thesystems with open boundaries in general space-time dimensions, we also analyzetheir implications under general duality implemented by the shift of defectscorresponding to generalized symmetries, including higher-form, non-invertiblesymmetries, in principle. Our formulation opens up a new paradigm to explorethe systems with protected edge modes in the established language of therenormalization group.

Protected edge modes based on the bulk and boundary renormalization group: A relationship between duality and generalized symmetry