Abstract
In this note we consider the set of line operators in theories of class S. We show that this set carries the action of a natural discrete dynamical system associated with the BPS spectrum. We discuss several applications of this perspective; the relation with global properties of the theory; the set of constraints imposed on the spectrum generator, in particular for the case of SU(2) mathcal{N} = 2*; and the relation between line defects and certain spherical Double Affine Hecke Algebras.
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