Proceedings_of Symposia in Pure Mathematics

Volume 62.2, 1997

Seiberg-Witten Integrable Systems

Ron Y. Donagi

Contents

Introduction

§1. Some physics background

Electromagnetism

Yang-Mills theory

Quantization

Supersymmetry

N = 2 super Yang-Mills

Duality

The Seiberg-Witten solution

Adding Matter

§2. Why integrable systems?

Algebraically integrable systems

Seiberg-Witten differentials

Linearity: complexified Duistermaat-Heckman

§3. Which integrable system?

Meromorphic Higgs bundles

The spectral curves

Elliptic solitons

Tests

Consistency with Seiberg-Witten

Mass to zero: the N=4 limit

T to oo: the flow to pure N=2

Higgs to oo: symmetry breaking

Singularities

§4. Other integrable systems

Pure N = 2 SYM

The Toda system

1991 Mathematics Subject Classification. Primary: 81T13, 81T60, 58F07.

Secondary: 14D20, 14H40.

Work partially supported by NSF grant DMS95-03249, and by grants from the

Univesity of Pennsylvania Research Foundation and The Harmon Duncombe Foundation.

© 1997 American Mathematical Society

http://dx.doi.org/10.1090/pspum/062.2/1492533