Title: Dualities in Gauge Theories and their Geometric Realization
Abstract: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,generali...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 are discussed such as the inclusion of hypermultiplets. Special emphasis is put onthe selfdualNf= 4 theory, which will play a central role in remainder. Furthermore, a briefsummary is given of the M-theory construction of Witten to determine the Seiberg-Witten curvesof gauge theories with arbitrary unitary product gauge groups, also dubbed quiver gauge theories.This provides the necessary introduction to understand the recent developments made by Gaiotto.Superconformal quiver theories are associated in a very precise manner to punctured RiemannsurfacesCn,g. Gaiotto’s conjecture that the UV moduli space of the quiver theories equals themoduli space of the associated Riemann surface is explained in detail. Furthermore, explicit checksof his proposal are performed by comparing the boundaries of the moduli spaces for Tn,g[A1],g= 0,1. We briefly re-examine the M-theory construction in this new light, essentially explainingthe reduction of the elusive 6d (2,0) theory onCn,g. At last, the extension toA2andAN−1quivergauge theories is discussed.Read More
Publication Year: 2020
Publication Date: 2020-09-07
Language: en
Type: article
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