Hitchin Equation, Singularity, and N=2 Superconformal Field Theories
Nov, 200941 pages
Published in:
- JHEP 03 (2010) 043
e-Print:
- 0911.1990 [hep-th]
Report number:
- ACT-11-09,
- MIFP-09-46
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Abstract: (arXiv)
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 theory on a punctured Riemann surface. We study the singular solution to Hitchin's equation and the Higgs field of solutions has a simple pole at the punctures/ We show that the massless theory is associated with Higgs field whose residual 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 the mass-deformed theory the residual 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 the 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.- Supersymmetric gauge theory
- Supersymmetry and Duality
- Brane Dynamics in Gauge Theories
- M-Theory
- field theory: conformal
- supersymmetry: 2
- dimension: 4
- gauge field theory: SU(2)
- symmetry: flavor
- dimension: 6
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