A note on discrete dynamical systems in theories of class $S$

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) $\mathcal{N}=2^{\ast }$; and the relation between line defects and certain spherical Double Affine Hecke Algebras.

33 pages, a Mathematica notebook is included with the paper; v2 minor changes, published version

References in corpus (5)

• On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics
• Line defect Schur indices, Verlinde algebras and $U(1{)}_r$ fixed points
• $q$-nonabelianization for line defects
• Quantum Line Defects and Refined BPS Spectra
• S duality and Framed BPS States via BPS Graphs

Cited by in corpus (1)

• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators