Seiberg-Witten theory for a non-trivial compactification from five to four dimensions

The prepotential and spectral curve are described for a smooth interpolation between an enlarged N=4 SUSY and ordinary N=2 SUSY Yang-Mills theory in four dimensions, obtained by compactification from five dimensions with non-trivial (periodic and antiperiodic) boundary conditions. This system provides a new solution to the generalized WDVV equations. We show that this exhausts all possible solutions of a given functional form.Comment: 10 pages, LaTeX, 2 figures using emlines.st

Quasiclassical Geometry and Integrability of AdS/CFT Correspondence

We discuss the quasiclassical geometry and integrable systems related to the gauge/string duality. The analysis of quasiclassical solutions to the Bethe anzatz equations arising in the context of the AdS/CFT correspondence is performed, compare to stationary phase equations for the matrix integrals. We demonstrate how the underlying geometry is related to the integrable sigma-models of dual string theory, and investigate some details of this correspondence.Comment: Based on talks at the conferences "Classical and quantum integrable systems", January 2004, Dubna, and "Quarks-2004", May 2004, Pushkinskie Gory, Russia; LaTeX, 17 pp, 3 figures; references adde

Exact solutions to quantum field theories and integrable equations

The exact solutions to quantum string and gauge field theories are discussed and their formulation in the framework of integrable systems is presented. In particular I consider in detail several examples of appearence of solutions to the first-order integrable equations of hydrodynamical type and stress that all known examples can be treated as partial solutions to the same problem in the theory of integrable systems.Comment: revised version, some details and formulations are changed, few references added; LaTeX, 12 p

Seiberg-Witten Curves and Integrable Systems

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.Comment: 17 pages, LaTeX; Talk at the Edinburgh conference "Integrability: the Seiberg-Witten and Whitham Equations", 14-19 September 199

SUSY gauge theories and Whitham integrable systems from compactification and SUSY breaking

We review the Seiberg-Witten construction of low-energy effective actions and BPS spectra in SUSY gauge theories and its formulation in terms of integrable systems. It is also demonstrated how this formulation naturally appears from the compactified version of the theory with partially broken supersymmetry so that the integrable structures arise from the relation between bare and quantum variables and superpotentials of SUSY gauge theories. The Whitham integrable systems, literally corresponding to the uncompactified theory, are then restored by averaging over fast variables in the decompactification limit.Comment: Contribution to the proceedings of the workshop "Gauge Theory and Integrable Systems", YITP, Kyoto, 26-29 January, 1999; 13pp, LaTe

Deformations of the root systems and new solutions to generalised WDVV equations

A special class of solutions to the generalised WDVV equations related to a finite set of covectors is investigated. Some geometric conditions on such a set which guarantee that the corresponding function satisfies WDVV equations are found (check-conditions). These conditions are satisfied for all root systems and their special deformations discovered in the theory of the Calogero-Moser systems by O.Chalykh, M.Feigin and the author. This leads to the new solutions for the generalized WDVV equations.Comment: 8 page