N=2gauge theories and degenerate fields of Toda theory

2009/11/30 by Shoichi Kanno, Yutaka Matsuo, Shotaro Shiba +1 · 5 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Degenerate energy levels #Gauge (firearms) #Gauge theory #Geology #Materials science #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Type (biology) #hep-th

paper · pdf · doi:10.1103/physrevd.81.046004

published as Phys.Rev.D81:046004,2010 · 23 pages,v2: minor corrections,published version

openalex publication_date 2010/02/24 · arxiv created 2010/04/22 · arxiv updated 2010/04/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We discuss the correspondence between degenerate fields of the W_N algebra and punctures of Gaiotto's description of the Seiberg-Witten curve of N=2 superconformal gauge theories. Namely, we find that the type of degenerate fields of the W_N algebra, with null states at level one, is classified by Young diagrams with N boxes, and that the singular behavior of the Seiberg-Witten curve near the puncture agrees with that of W_N generators. We also find how to translate mass parameters of the gauge theory to the momenta of the Toda theory.

Citations

• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• THE MODELS OF TWO-DIMENSIONAL CONFORMAL QUANTUM FIELD THEORY WITH Zn SYMMETRY
• W-symmetry in Conformal Field Theory
• Wall-crossing, Hitchin systems, and the WKB approximation

Cited by

• Gauge theory Wilson loops and conformal Toda field theory
• 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
• On AGT description of N = 2 SCFT with N f = 4
• Compactification on the Ω-background and the AGT correspondence

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