Canonical bases for Coulomb branches of 4d N=2 gauge theories

2023/06/05 by Cautis, Sabin, Williams, Harold
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2306.03023

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 R_G,N, where N is a representation of a reductive group G. Its heart KP_G,N is a finite-length, rigid, monoidal abelian category with renormalized r-matrices. We refer to objects of KP_G,N as Koszul-perverse coherent sheaves. Simple objects of 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 N=2 gauge theory of cotangent type.

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