Seiberg-Witten theory, matrix model and AGT relation

2010/06/15 by Tohru Eguchi, Kazunobu Maruyoshi
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Chemistry #Computer science #Data mining #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix model #Noncommutative and Quantum Gravity Theories #Pure mathematics #Relation (database) #hep-th

paper · pdf · doi:10.1007/jhep07(2010)081

published as JHEP 1007:081,2010 · 19 pages, 1 figure

arxiv created 2010/06/15 · openalex publication_date 2010/07/01 · arxiv updated 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We discuss the Penner-type matrix model which has been proposed to explain the AGT relation between the 2-dimensional Liouville theory and 4-dimensional N=2 superconformal gauge theories. In our previous communication we have obtained the spectral curve of the matrix model and showed that it agrees with that derived from M-theory. We have also discussed the decoupling limit of massive flavors and proposed new matrix models which describe Seiberg-Witten theory with flavors N_f=2,3. In this article we explicitly evaluate the free energy of these matrix models and show that they in fact reproduce the amplitudes of Seiberg-Witten theory.

Citations

• Zamolodchikov asymptotic formula and instanton expansion in 𝒩 = 2 SUSYNf= 2NcQCD
• Infinite conformal symmetry in two-dimensional quantum field theory
• On N = 2 supersymmetric QCD with four flavors
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N = 2 dualities
• PREPOTENTIALS OF N=2 SUPERSYMMETRIC GAUGE THEORIES AND SOLITON EQUATIONS
• Wall-crossing, Hitchin systems, and the WKB approximation
• Wall-crossing, Hitchin Systems, and the WKB Approximation