2010/06/30 by Wei He, Yan-Gang Miao · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Dyon #Effective action #Gauge theory #Hypergeometric function #Instanton #Integrable system #Magnetic monopole #Mathematical physics #Mathematics #Moduli space #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantization (signal processing) #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #hep-th
paper · pdf · doi:10.1103/physrevd.82.025020
published as Phys.Rev.D82:025020,2010 · 17 pages, submitted to PRD; v2, typos corrected, references added; v3, published version
openalex publication_date 2010/07/29 · arxiv created 2010/07/31 · arxiv updated 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is recently claimed by Nekrasov and Shatashvili that the N=2 gauge theories in the \ensuremathΩ background with ϵ1=\ensuremathℏ, ϵ2=0 are related to the quantization of certain algebraic integrable systems. We study the special case of SU(2) pure gauge theory; the corresponding integrable model is the A1 Toda model, which reduces to the sine-Gordon quantum mechanics problem. The quantum effects can be expressed as the WKB series written analytically in terms of hypergeometric functions. We obtain the magnetic and dyonic expansions of the Nekrasov theory by studying the property of hypergeometric functions in the magnetic and dyonic regions on the moduli space. We also discuss the relation between the electric-magnetic duality of gauge theory and the action-action duality of the integrable system.