Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-01-08
Nucl.Phys.B530:73-98,1998
Physics
High Energy Physics
High Energy Physics - Theory
revised version, appendix E is enlarged, references are added, latex, 32 pages, 1 figure, documentstyle[12pt,eclepsf,a4]{artic
Scientific paper
10.1016/S0550-3213(98)00407-6
Five dimensional supersymmetric gauge theory compactified on a circle defines an effective N=2 supersymmetric theory for massless fields in four dimensions. Based on the relativistic Toda chain Hamiltonian proposed by Nekrasov, we derive the Picard-Fuchs equation on the moduli space of the Coulomb branch of SU(2) gauge theory. Our Picard-Fuchs equation agrees with those from other approaches; the spectral curve of XXZ spin chain and supersymmetric cycle in compactified M theory. By making use of a relation to the Picard-Fuchs equation of SU(2) Seiberg-Witten theory, we obtain the prepotential and the effective coupling constant that incorporate both a perturbative effect of Kaluza-Klein modes and a non-perturbative one of four dimensional instantons. In the weak coupling regime we check that the prepotential exhibits a consistent behavior in large and small radius limits of the circle.
Kanno Hiroaki
Ohta Yuji
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