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Bibliographic Details
Main Author: Sakai, Kazuhiro
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2304.04878
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Table of Contents:
  • We study the E-string theory on $\mathbb{R}^4\times T^2$ 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 $\mathcal{N}=2$ supersymmetric $\mathrm{SU}(2)$ 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.