Non-invertible symmetries along 4d RG flows

TL;DR

<p>The paper investigates how non-invertible self-duality symmetries, realized by duality defects in 4d gauge theories, survive RG flows triggered by mass deformations. It develops a framework starting from 4d ${\mathcal N}=4$ SYM with gauge algebra ${\mathfrak{su}}(N)$ and tracks the fate of self-duality defects along ${\mathcal N}=1$ preserving flows to ${\mathcal N}=1^*$ and beyond, including gapped vacua described by 1-form symmetry TQFTs and their spontaneous symmetry breaking. It provides a comprehensive classification of vacua for ${\mathfrak{su}}(N)$, maps duality actions to TQFT data, and demonstrates that non-invertible duality defects can act nontrivially across gapped vacua, including spontaneous breaking and domain-wall interpolations between distinct 1-form phases; it also extends to ${\mathcal N}=2$ theories via class ${\mathcal S}$ constructions and to the conifold via holography and Seiberg duality. The results illuminate how non-invertible symmetries constrain IR physics, organize vacua into duality orbits, and persist under a broad class of mass deformations, with holographic and class ${\mathcal S}$ perspectives supporting the field-theoretic picture.

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 $\mathcal{N}=1^*$ 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.