We discuss various properties of the Seiberg-Witten curve for the E-string theory which we have obtained recently in hep-th/0203025. Seiberg-Witten curve for the E-string describes the low-energy dynamics of a six-dimensional (1, 0) SUSY theory when compactified on R 4 T 2 . It has a manifest affine E 8 global symmetry with modulus and E 8 Wilson line parameters {m i }, i = 1, 2, . . . , 8 which are associated with the geometry of the rational elliptic surface. When the radii R 5 , R 6 of the torus T 2 degenerate R 5 , R 6 0, E-string curve is reduced to the known Seiberg-Witten curves of four-and five-dimensional gauge theories.
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Eguchi et al. (2003) studied this question.