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Picard-Fuchs Equation and Prepotential of Five Dimensional SUSY Gauge Theory Compactified on a Circle | | Hiroaki Kanno
; Yuji Ohta
; | | Date: |
8 Dec 1997 | | Journal: | Nucl.Phys. B530 (1998) 73-98 | | Subject: | hep-th | | Affiliation: | Dept. Math., Hiroshima Univ.) and Yuji Ohta (Res. Inst. Math. Sci., Kyoto Univ. | | Abstract: | 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. | | Source: | arXiv, hep-th/9801036 | | Services: | Forum | Review | PDF | Favorites | |
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