What question did this study set out to answer?

The work aims to develop a formalism that describes the renormalization group flow related to Schur indices and fusion algebras in supersymmetric theories.

February 8, 2026Journal of High Energy Physics0 citationsOpen Access

Renormalization Group Flow in Schur quantization

FAFederico Ambrosino DGDavide Gaiotto

Key Points

The work aims to develop a formalism that describes the renormalization group flow related to Schur indices and fusion algebras in supersymmetric theories.
Development of a general formalism for Schur quantization
Analysis of BPS indices in four-dimensional N=2 supersymmetric field theories
Extension of known results from Seiberg-Witten theory
Successfully describes the spectrum of BPS particles in N=2 gauge theories
Links spectra of BPS particles to pure N=2 gauge theories
Explores implications for quantum groups and cluster varieties

Abstract

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.

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