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N=2 supersymmetric QCD and elliptic potentials
We investigate the relation between the four dimensional N=2 SU(2) super
Yang-Mills theory with four fundamental flavors and the quantum mechanics model
with Treibich-Verdier potential described by the Heun equation in the elliptic
form. We study the precise correspondence of quantities in the gauge theory and
the quantum mechanics model. An iterative method is used to obtain the
asymptotic expansion of the spectrum for the Schr\"{o}dinger operator, we are
able to fix the precise relation between the energy spectrum and the instanton
partition function of the gauge theory. We also study asymptotic expansions for
the spectrum which correspond to the strong coupling regions of the
Seiberg-Witten theory.Comment: Latex, 29pp, published version, content restructured and simplifie
Rejoinder: Conditional Growth Charts
Rejoinder: Conditional Growth Charts [math.ST/0702634]Comment: Published at http://dx.doi.org/10.1214/009053606000000678 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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