Unit:
Κατεύθυνση Πυρηνική Φυσική και Φυσική Στοιχειωδών ΣωματιδίωνLibrary of the School of Science
Author:
Chatzis Dimitrios
Supervisors info:
Γεώργιος Διαμάντης, Αναπληρωτής Καθηγητής, Σχολή Θετικών Επιστημών τμήμα Φυσικής τομέας Πυρηνικής Φυσικής και Φυσικής Στοιχειωδών Σωματιδίων, ΕΚΠΑ.
Original Title:
Εισαγωγή στο Δυϊσμό Seiberg-Witten
Translated title:
Introduction to Seiberg-Witten Duality
Summary:
This thesis provides an introductory study of Seiberg-Witten duality, presenting the solution to the problem of determining the Lagrangian of the low energy degrees of freedom in an SU(2) Yang-Mills theory with N = 2 supersymmetry, as it was written by Seiberg and Witten. The first part gives an introduction to global supersymmetry, focusing mainly on the spectrum of supersymmetric theories and the construction of N = 2 supersymmetric Lagrangians. The gauge and matter representations are presented for N = 1, 2 and supersymmetric Yang-Mills theories are studied using superspace techniques. The second part concerns the existence of magnetic monopoles in gauge theories and their characteristics, as well as a study of duality transformations in such theories, where emphasis is given on the exchange of perturbative and non-perturbative sectors under duality, providing a map of the theory at strong(weak) coupling to weak(strong) coupling. The last part of the thesis solves the problem exactly by studying the Moduli space of vacuua in the model of an SU(2) N = 2 supersymmetric Yang-Mills theory, which features breaking of the gauge symmetry SU(2) → U(1) at some energy scale, below which the theory is abelian and the low energy degrees of freedom that survive are described by the Wilsonian action. After the solution through eliptic curves given by Seiberg and Witten is presented, a solution using differential equations is also provided, which gives off expressions of the various quantities through hypergeometric functions.
Main subject category:
Science
Keywords:
Quantum Field Theory, Supersymmetry, Duality, Gauge Theories, Yang-Mills Theories, Non Perturbative Phenomena.
