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
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