Non-invertible symmetries along 4d RG flows

Abstract

Abstract We explore novel examples of RG flows preserving a non-invertible self-duality symmetry. Our main focus is on $$ \mathcal{N} $$ N = 1 quadratic superpotential deformations of 4d $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory with gauge algebra $$ \mathfrak{su}(N) $$ su N . A theory that can be obtained in this way is the so-called $$ \mathcal{N} $$ 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 $$ \mathcal{S} $$ S , to demonstrate how non-invertible self-duality symmetries exist in a variety of $$ \mathcal{N} $$ N = 1 SCFTs. We finally apply this understanding to prove that the conifold theory has a non-invertible self-duality symmetry.