Non-invertible symmetries along 4d RG flows

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.Comment: 48 pages + appendices. v2: refs added and typos correcte

Reducible second-class constraints of order L: An irreducible approach

An irreducible canonical approach to second-class constraints reducible of an arbitrary order is given. This method generalizes our previous results from [Europhys. Lett. 50 (2000) 169, J. Phys. A: Math. Theor. 40 (2007) 14537] for first- and respectively second-order reducible second-class constraints. The general procedure is illustrated on Abelian gauge-fixed p-forms

Dynamic disturbance decoupling of nonlinear systems and linearization

In this paper we investigate the connections between the solvability of the dynamic disturbance decoupling problem with exponential stability (DDDPes) for a nonlinear system and the solvability of the same problem for its linearization around an equilibrium point. It is shown that under generic conditions the nonlinear DDDPes is solvable for a nonlinear system if and only if the static disturbance decoupling problem with stability (DDPs) is solvable for its linearization around an equilibrium point