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A bstract We explore novel examples of RG flows preserving a non-invertible self-duality symmetry. Our main focus is on N N = 1 quadratic superpotential deformations of 4d N N = 4 super-Yang-Mills theory with gauge algebra su (N) su N. A theory that can be obtained in this way is the so-called N N = 1 * SYM where all adjoint chiral multiplets have a mass. Such IR theory exhibits a rich structure of vacua which we thoroughly examine. Our analysis elucidates the physics of spontaneous breaking of self-duality symmetry occurring in the degenerate gapped vacua. The construction can be generalized, taking as UV starting point a theory of class S S, to demonstrate how non-invertible self-duality symmetries exist in a variety of N N = 1 SCFTs. We finally apply this understanding to prove that the conifold theory has a non-invertible self-duality symmetry.
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