Hitchin Equation, Irregular Singularity, and N=2 Asymptotical Free Theories

2010/05/08 by Dimitri V. Nanopoulos, Dimitri Nanopoulos, Dan Xie +2 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #hep-th

paper · pdf · doi:10.48550/arxiv.1005.1350

37 pages, 6 figures

arxiv created 2010/05/08 · openalex publication_date 2010/05/08 · arxiv updated 2010/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study irregular singular solution to Hitchin's equation and use it to describe four dimensional N=2 asymptotically free gauge theories. For SU(2) A type quiver, two kinds of irregular singularities besides one regular singularity are needed for the solution of Hitchin's equation; We then classify irregular singularities needed for the general SU(N) A type quiver.

Citations

• The Self-Duality Equations on a Riemann Surface
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• The power of Nekrasov functions
• Zamolodchikov asymptotic formula and instanton expansion in 𝒩 = 2 SUSYNf= 2NcQCD
• S-duality and 2d topological QFT
• A Hyper-KÄHlerian Structure on Coadjoint Orbits of a Semisimple Complex Group
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality
• Gauge Theory, Ramification, And The Geometric Langlands Program
• Wall-crossing, Hitchin Systems, and the WKB Approximation

Cited by

• The BPS spectrum generator in 2D-4D systems
• TOWARDS A PROOF OF AGT CONJECTURE BY METHODS OF MATRIX MODELS
• Analysis of correlation functions in Toda theory and the Alday-Gaiotto-Tachikawa-Wyllard relation forSU(3)quiver

Related

• Hitchin systems in N=2 field theory
• A tentative proposal towards an equivariant mirror symmetry for Hitchin systems
• Deconstructing Deformed D-quivers
• Quiver Asymptotics: N=1 Free Chiral Ring
• 4d N=2 SCFT and singularity theory Part I: Classification