Seiberg-Witten Curves and Integrable Systems

Talk presented by the second author at the Inaugural Coference of the Asia Pacific Center for Theoretical Physics, Seoul, June 1996. The purpose of this note is to give a resume of the Seiberg-Witten theory in the simplest possible mathematical terms.

This is a very brief review of relations between Seiberg-Witten theories and integrable systems with emphasis on the perturbative prepotentials presented at the E.S.Fradkin Memorial Conference.

These lectures are devoted to the low energy limit of \N2 SUSY gauge theories, which is described in terms of integrable systems. A special emphasis is on a duality that naturally acts on these integrable systems. The duality turns out to be an effective tool in constructing the double elliptic integrable system which describes the six-dimensional Seiberg-Witten theory. At the same time, it implies a series of relations between other Seiberg-Witten systems.

These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.

These notes provide an introductory exposition of the Seiberg-Witten gauge theory. They collect the material presented in a series of seminars given by the author at the University of Milano.

In this note it is demonstrated how the Seiberg-Witten solutions and related integrable systems may arise from certain brane configurations in M-theory. Some subtleties of the formulation of the Seiberg-Witten theory via integrable systems are discussed and interpreted along the lines of general picture of string/M-theory dualities.

This is a survey of the work of Seiberg and Witten on 4-dimensional N=2 supersymmetric Yang-Mills theory and of some of its recent extensions, written for mathematicians. The point of view is that of algebraic geometry and integrable systems. An introductory chapter tries to describe some of the relevant physics for a reader with no physics background. This is followed by a review of the relevant properties of integrable systems. The remaining chapters describe the specific i...

In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.

In this note, we give an exposition of the construction of Seiberg-Witten invariants.

Recent developments in Seiberg-Witten theory and relations with Complex Geometry.