Dualities in Gauge Theories and their Geometric Realization

摘要: In this thesis, exact results inN= 2 super Yang-Mills theories are discussed. Starting from theexact solution of pure SYM provided by Seiberg and Witten through an elliptic curve construction,generalizations discussed such as the inclusion hypermultiplets. Special emphasis is put onthe selfdualNf= 4 theory, which will play a central role in remainder. Furthermore, briefsummary given M-theory construction to determine Seiberg-Witten curvesof gauge with arbitrary unitary product groups, also dubbed quiver theories.This provides necessary introduction understand recent developments made Gaiotto.Superconformal associated very precise manner punctured RiemannsurfacesCn,g. Gaiotto’s conjecture that UV moduli space equals themoduli Riemann surface explained detail. explicit checksof his proposal performed comparing boundaries spaces for Tn,g[A1],g= 0,1. We briefly re-examine new light, essentially explainingthe reduction elusive 6d (2,0) theory onCn,g. At last, extension toA2andAN−1quivergauge