Renormalization Group Flow in Schur quantization

A bstract We develop a general formalism to describe the Renormalization Group Flow of Schur indices and fusion algebras of BPS line defects in four-dimensional 𝒩 = 2 Supersymmetric Quantum Field Theories. The formalism includes and extends known results about the Seiberg-Witten description of these structures. Another application of the formalism is to describe the spectrum of BPS partices of 𝒩 = 2 gauge theories with matter in terms of the spectrum of pure 𝒩 = 2 gauge theories. Applications to the theory of quantum groups and to the quantization of cluster varieties are also discussed.