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Over the past decade, our understanding of symmetries in quantum field theory has undergone a significant reformulation. A key insight is that global symmetries in QFT can be characterized by the existence of topological operators that commute with the Hamiltonian. This perspective naturally leads to two broad classes of generalized symmetries. The first consists of higher-form symmetries, where symmetry operators act on extended objects rather than local operators, while still forming a group structure. The second comprises non-invertible symmetries, for which the symmetry operators no longer form a group but instead organize into a categorical structure.
These generalized notions of symmetry have found a wide range of applications across diverse areas of physics, including high-energy theory, condensed matter systems, lattice field theory and even astrophysical contexts. In this talk, we focus on recent developments that exploit these symmetries to probe entanglement properties in two-dimensional conformal field theories. In particular, we discuss how entanglement can be resolved with respect to 0-form non-invertible symmetries, and what physical information such symmetry-resolved entanglement captures. We will present two complementary approaches to this problem: one based on boundary conformal field theory (BCFT) techniques, and another employing twist-field constructions. |