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We study the E-string theory on Double-struck capital R-4 x T-2 with Wilson lines. We consider two examples where interesting automorphisms arise. In the first example, the spectrum is invariant under the F-4 Weyl group acting on the Wilson line parameters. We obtain the Seiberg-Witten curve expressed in terms of Weyl invariant F-4 Jacobi forms. We also clarify how it is related to the thermodynamic limit of the Nekrasov-type formula. In the second example, the spectrum is invariant under the D-4 triality combined with modular transformations, the automorphism originally found in the 4d MATHEMATICAL SCRIPT CAPITAL N � = 2 supersymmetric SU(2) gauge theory with four massive flavors. We introduce the notion of triality invariant Jacobi forms and present the Seiberg-Witten curve in terms of them. We show that this Seiberg-Witten curve reduces precisely to that of the 4d theory with four flavors in the limit of T-2 shrinking to zero size.
Keyword:
Field Theories in Higher Dimensions
Global Symmetries
Supersymmetric Gauge Theory
期刊
IF:
5.5
论文数:
4.0W
被引数:
13.7W
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