Abstract
By carrying out a rational transformation on the base curve C P 1 of the Seiberg–Witten curve for N = 2 supersymmetric pure SU ( 2 ) -gauge theory, we obtain a family of Jacobian elliptic K3 surfaces of Picard rank 17 . The isogeny relating the Seiberg–Witten curve for pure SU ( 2 ) -gauge theory to the one for SU ( 2 ) -gauge theory with N f = 2 massless hypermultiplets extends to define a Nikulin involution on each K3 surface in the family. We show that the desingularization of the quotient of the K3 surface by the involution is isomorphic to a Kummer surface of the Jacobian variety of a curve of genus two. We then derive a relation between the Yukawa coupling associated with the elliptic K3 surface and the Yukawa coupling of pure SU ( 2 ) -gauge theory.
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