Hitchin equation, singularity, and N = 2 superconformal field theories View Full Text


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Article Info

DATE

2010-03

AUTHORS

Dimitri Nanopoulos, Dan Xie

ABSTRACT

We argue that Hitchin’s equation determines not only the low energy effective theory but also describes the UV theory of four dimensional N = 2 superconformal field theories when we compactify six dimensional AN (0, 2) theory on a punctured Riemann surface. We study singular solutions to Hitchin’s equation and the Highs field of equation has a simple pole at the punctures; We show that the massless theory is associated with Higgs field whose residue is a nilpotent element; We identify the flavor symmetry associated with the puncture by studying the singularity of closure of the moduli space of solutions with the appropriate boundary conditions. For mass-deformed theory the residue of the Higgs field is a semi-simple element, we identify the semi-simple element by arguing that the moduli space of solutions of mass-deformed theory must be a deformation of the closure of the moduli space of massless theory. We also study the Seiberg-Witten curve by identifying it as the spectral curve of the Hitchin’s system. The results are all in agreement with Gaiotto’s results derived from studying the Seiberg-Witten curve of four dimensional quiver gauge theory. More... »

PAGES

43

References to SciGraph publications

  • 2009-12-10. Recursion relations in CFT and N=2 SYM theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-02. Liouville Correlation Functions from Four-Dimensional Gauge Theories in LETTERS IN MATHEMATICAL PHYSICS
  • 2009-09-18. New Seiberg dualities from 𝒩 = 2 dualities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-11-04. AN−1 conformal Toda field theory correlation functions from conformal 𝒩 = 2 SU(N) quiver gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01. Five-dimensional AGT conjecture and the deformed Virasoro algebra in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-07-20. Six-dimensional DN theory and four-dimensional SO-USp quivers in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-08-27. N = 2 SU quiver with USP ends or SU ends with antisymmetric matter in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01. Loop and surface operators in gauge theory and Liouville modular geometry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-12-28. S-duality in N = 2 supersymmetric gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-09-09. Webs of five-branes and 𝒩 = 2 superconformal field theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-11-10. Zamolodchikov asymptotic formula and instanton expansion in 𝒩 = 2 SUSY Nf = 2Nc QCD in JOURNAL OF HIGH ENERGY PHYSICS
  • 1980-10. Minimal singularities inGLn in INVENTIONES MATHEMATICAE
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