|Abstract: Certain Quantum Field Theories exhibit self-dualities: the same physics has two mutually non-local descriptions which are nevertheless very similar, with the difference lying only in the values of certain parameters and the global structure. Well-known examples include N=4 SYM in four dimensions and the Ising CFT in two dimensions. In certain situations, self-duality can be turned into an actual symmetry of a physical theory, often at the cost of rendering it non-invertible. In this talk, I will describe various aspects of these non-invertible self-duality symmetries. Specifically, I will explain how they are captured by the holographic dual description when one exists, and what the dynamical implications of the symmetry are. As a result of the analysis, it becomes evident that non-invertibility is more than just a subtle detail; it can sometimes be viewed as an anomaly with dramatic consequences for any symmetry-preserving RG flow.
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