136 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
Integrability and Seiberg-Witten Exact Solution
The exact Seiberg-Witten (SW) description of the light sector in the
SUSY Yang-Mills theory is reformulated in terms of integrable systems and
appears to be a Gurevich-Pitaevsky (GP) solution to the elliptic Whitham
equations. We consider this as an implication that dynamical mechanism behind
the SW solution is related to integrable systems on the moduli space of
instantons. We emphasize the role of the Whitham theory as a possible
substitute of the renormalization-group approach to the construction of
low-energy effective actions.Comment: Latex, figs include
p,q-Duality and Hamiltonian Flows in the Space of Integrable Systems or Integrable Systems as Canonical Transforms of the Free Ones
Variation of coupling constants of integrable system can be considered as
canonical transformation or, infinitesimally, a Hamiltonian flow in the space
of such systems. Any function generates a one-parametric
family of integrable systems in vicinity of a single system: this gives an idea
of how many integrable systems there are in the space of coupling constants.
Inverse flow is generated by a dual "Hamiltonian", associated with the dual integrable system. In vicinity of a self-dual
point the duality transformation just interchanges momenta and coordinates in
such a "Hamiltonian": . For
integrable system with several coupling constants the corresponding
"Hamiltonians" satisfy Whitham equations and after
quantization (of the original system) become operators satisfying the
zero-curvature condition in the space of coupling constants: [ d/dg_a -
T_a(p,q), d/dg_b - T_b(p,q) ] = 0. Some explicit formulas are given for
harmonic oscillator and for Calogero-Ruijsenaars-Dell system.Comment: LaTeX, 16 pages (acknowledgements improved
SUSY field theories, integrable systems and their stringy/brane origin -- II
Five and six dimensional SUSY gauge theories, with one or two compactified
directions, are discussed. The 5d theories with the matter hypermultiplets in
the fundamental representation are associated with the twisted spin
chain, while the group product case with the bi-fundamental matter corresponds
to the higher rank spin chains. The Riemann surfaces for theories with
fundamental matter and two compact directions are proposed to correspond to the
spin chain based on the Sklyanin algebra. We also discuss the obtained
results within the brane and geometrical engeneering frameworks and explain the
relation to the toric diagrams.Comment: LaTeX, 21 pages, no figure
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