537 research outputs found
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
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
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
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
Associativity Equations in Effective SUSY Quantum Field Theories
The role of associativity or WDVV equations in effective supersymmetric
quantum theories is discussed and it is demonstrated that for wide class of
their solutions when residue formulas are valid the proof of associativity
equations can be reduced to solving the system of ordinary linear equations and
depends only upon corresponding matching and nondegeneracy conditions. The
covariance of WDVV equations upon generic duality transformations and the role
of associativity equations in general context of quasiclassical integrable
systems is also discussed.Comment: Contribution to the proceedings of the conference SUSY01, Dubna, June
2001; LaTeX, 8 p
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
Non-perturbative Quantum Theories and Integrable Equations
I review the appearance of classical integrable systems as an effective tool
for the description of non-perturbative exact results in quantum string and
gauge theories. Various aspects of this relation: spectral curves, action-angle
variables, Whitham deformations and associativity equations are considered
separately demonstrating hidden parallels between topological 2d string
theories and naively non-topological 4d theories. The proofs are supplemented
by explicit illustrative examples.Comment: 35 pages, LaTeX, to appear in Int.J.Mod.Phys.
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