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

Keywords

• Duality in Gauge Field Theories
• Supersymmetric Gauge Theory
• Discrete Symmetries