Generalized Seiberg-Witten and the Nahm Transform

by Robin Raymond
Doctoral thesis
Date of Examination:2018-01-24
Date of issue:2019-01-11
Advisor:Prof. Dr. Viktor Pidstrygach
Referee:Prof. Dr. Viktor Pidstrygach
Referee:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Karl-Henning Rehren
Referee:Prof. Dr. Henrik Seppänen
Referee:Prof. Dr. Max Wardetzky
Referee:Prof. Dr. Chenchang Zhu
Persistent Address: http://dx.doi.org/10.53846/goediss-7232

 

 

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Abstract

English

Using the viewpoint of principal bundles on hyperk¨ ahler reductions, we recover the results of Gocho and Nakajima [GN92] and give insights into the role that the quater- nions play. We define a framework for dimensional reduction of gauge theories and show that the Haydys-Witten equations are dimensionally reduced Spinp7q-instantons. We extend the Nahm transform to data close to a solution satisfying the ordinary boundary conditions. Using generalized Seiberg-Witten, we show that G2-Monopoles on Λ2 `X and solutions of the Haydys-Witten equations on R ˆ X for X an oriented Riemannian 4-manifold are related to solutions of generalized Seiber-Witten equations with target the moduli space of Bogomolny monopoles and Nahm equations respec- tively. Applying the Nahm transform we derive a relation between G2-Monopoles and solutions of the Haydys-Witten equations. Finally we hint how this can be extended
Keywords: Gauge Theory; Nahm Transform; Generalized Seiberg-Witten
 
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