Seiberg - Witten Curves and Integrable Systems 1
نویسنده
چکیده
This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of Seiberg-Witten curves in terms of corresponding integrable models.
منابع مشابه
Seiberg - Witten Theory , Integrable Systems and D - branes ∗
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 os string/M-theory dualities.
متن کاملDuality in Integrable Systems and Generating Functions for New Hamiltonians
Duality in the integrable systems arising in the context of Seiberg-Witten theory shows that their tau-functions indeed can be seen as generating functions for the mutually Poisson-commuting hamiltonians of the dual systems. We demonstrate that the Θ-function coefficients of their expansion can be expressed entirely in terms of the co-ordinates of the Seiberg-Witten integrable system, being, th...
متن کاملOn Integrable Systems and Supersymmetric Gauge Theories
The properties of theN = 2 SUSY gauge theories underlying the Seiberg-Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential are presented, the invariant sense of these definitions is illustrated. Recently found exact nonperturbative solutions to N = 2 SUSY gauge theori...
متن کاملOn Integrable Systems and Supersymmetric Gauge Theories
The properties of theN = 2 SUSY gauge theories underlying the Seiberg-Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential are presented, the invariant sense of these definitions is illustrated. Recently found exact nonperturbative solutions to N = 2 SUSY gauge theori...
متن کاملSeiberg - Witten Systems and Whitham Hierarchies : a Short Review
We briefly review the Whitham hierarchies and their applications to integrable systems of the Seiberg-Witten type. The simplest example of the N = 2 supersymmet-ric SU (2) pure gauge theory is considered in detail and the corresponding Whitham solutions are found explicitely.
متن کامل