Non-invertible symmetries along 4d RG flows

Abstract

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

48 pages + appendices. v2: refs added and typos corrected

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• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• When the moduli space is an orbifold: Spontaneous breaking of continuous non-invertible symmetries
• Boundary SymTFT
• Symmetry fractionalization and duality defects in Maxwell theory
• Twisted Partition Functions as Order Parameters
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Global variants of $\mathcal{N}=1^{\ast }$ theories and Calogero-Moser systems