$K_{\mathfrak{q}}$-algebras

Davide Gaiotto

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arXiv · 2609.38702

$K_{\mathfrak{q}}$-algebras

Davide Gaiotto

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Abstract

We introduce the notion of $K_{\mathfrak{q}}$-algebra, a conjectural axiomatization of the fusion algebra of rotation-equivariant BPS line defects in a 4d ${\cal N}=2$ Supersymmetric Quantum Field Theory. We also introduce the notion of RG flow of $K_{\mathfrak{q}}$-algebras, a conjectural axiomatization of the action of Seiberg-Witten type RG flows on line defects. These definitions enrich the theory of cluster algebras, $K$-theoretic Coulomb branch algebras, skein algebras and quantum groups.

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Davide Gaiotto. 2026-09-30. $K_{\mathfrak{q}}$-algebras. https://arxiv.org/abs/2609.38702

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