Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality

2023/07/23 by Davide Gaiotto, Gaiotto, Davide · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2307.12396

openalex publication_date 2023/07/23 · openalex created_date 2023/07/26 · openalex updated_date 2026/07/28

Abstract

We employ the protected sphere correlation functions of three-dimensional Super Conformal Field Theories with eight supercharges in order to define a quantization of their Higgs and Coulomb branches of vacua as real phase spaces. We also employ hemisphere correlation functions to define a quantization of certain real loci in the Higgs and Coulomb branches. Localization formulae and dualities applied to these quantizations result in a body of predictions about unitary representations of certain algebras, which may perhaps be understood as an ``analytic'' form of the symplectic duality program. In particular, the protected correlation functions in the class of theories denoted as T[G] are naturally related to the theory of unitary representations of complex or real semi-simple Lie groups.

Cited by

• Positive traces on quantized abelian Coulomb branches
• Analytical Traces on Coulomb Branches of Quiver Gauge Theories
• Positive traces on certain SL(2) Coulomb branches

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