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arXiv · 2306.03023

Canonical bases for Coulomb branches of 4d $\mathcal{N}=2$ gauge theories

Sabin Cautis·Harold Williams
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Abstract

We construct and study a nonstandard t-structure on the derived category of equivariant coherent sheaves on the Braverman-Finkelberg-Nakajima space of triples $\mathcal{R}_{G,N}$, where $N$ is a representation of a reductive group $G$. Its heart $\mathcal{KP}_{G,N}$ is a finite-length, rigid, monoidal abelian category with renormalized $r$-matrices. We refer to objects of $\mathcal{KP}_{G,N}$ as Koszul-perverse coherent sheaves. Simple objects of $\mathcal{KP}_{G,N}$ define a canonical basis in the quantized $K$-theoretic Coulomb branch of the associated gauge theory. These simples possess various characteristic properties of Wilson-'t Hooft lines, and we interpret our construction as an algebro-geometric definition of the category of half-BPS line defects in a 4d $\mathcal{N}=2$ gauge theory of cotangent type.

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Sabin Cautis, Harold Williams. 2023-06-05. Canonical bases for Coulomb branches of 4d $\mathcal{N}=2$ gauge theories. https://arxiv.org/abs/2306.03023

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