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- W3100973397 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 $A_N$ $(0,2)$ 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." @default.
- W3100973397 created "2020-11-23" @default.
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- W3100973397 date "2010-03-01" @default.
- W3100973397 modified "2023-09-26" @default.
- W3100973397 title "Hitchin equation, singularity, and N = 2 superconformal field theories" @default.
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- W3100973397 doi "https://doi.org/10.1007/jhep03(2010)043" @default.
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