The Geometry and Physics of the Seiberg—Witten Equations

Chapter
Part of the Progress in Mathematics book series (PM, volume 205)

Abstract

These lectures are aimed at explaining the physical origin of the Seiberg—Witten equations and invariants to a mathematical audience. In the course of the exposition, we will cover several rich aspects of nonperturbative quantum field theory. Attempts have been made to reduce the prerequisites to a minimum and to provide a comprehensive bibliography. Lecture 1 explains classical and quantum pure gauge theory and its supersymmetric versions, with a digression on supersymmetry. Emphasis is on the non-perturbative aspects of field theories, such as vacuum structure, existence of mass gap, symmetries, and anomalies. Lecture 2 is about the duality conjecture in (supersymmetric) gauge theories and its consequences. It begins with the notion of duality and the role monopoles play in electric-magnetic duality. Lecture 3 reviews Donaldson invariants and topological field theory, followed by the low energy solution to theN =2 supersymmetric gauge theory by Seiberg and Witten, and its application to four-manifolds.

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© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Siye Wu
    • 1
  1. 1.Department of Pure MathematicsUniversity of AdelaideAdelaideAustralia

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