Functoriality of Coulomb branches

2025/01/17 by Tom Gannon, Ben Webster, Gannon, Tom +1 · 2 citations
Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2501.09962

openalex publication_date 2025/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the affine closure of the cotangent bundle of the parabolic base affine space for GL_n or SL_n is a Coulomb branch, which confirms a conjecture of Bourget-Dancer-Grimminger-Hanany-Zhong. In particular, we show that the algebra of functions on the cotangent bundle of the parabolic base affine space of GL_n or SL_n is finitely generated. We prove this by showing that, if we are given a map H → G of complex reductive groups and a representation of G satisfying an assumption we call gluable, then the Coulomb branch for the induced representation of H is obtained from the corresponding Coulomb branch for G by a certain Hamiltonian reduction procedure. In particular, we show that the Coulomb branch associated to any quiver with no loops can be obtained from Coulomb branches associated to quivers with exactly two vertices using this procedure.

Cited by

• Rankin-Selberg duality via gluing
• Intersections of twisted cotangent bundles and symplectic duality

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