Seiberg-Witten prepotential for E-string theory and global symmetries

TL;DR

This paper derives Nekrasov-type formulas for the Seiberg-Witten prepotential of the six-dimensional E-string theory with Wilson lines, revealing connections to elliptic Nekrasov partition functions and SU(2) gauge theories with four flavors.

Contribution

It provides new Nekrasov-type expressions for the E-string theory's prepotential with general Wilson lines and clarifies its relation to SU(2) Seiberg-Witten theory with N_f=4.

Findings

Derived Nekrasov-type formulas for various unbroken global symmetries.

Connected E-string theory prepotential to elliptic Nekrasov partition functions.

Presented a new Seiberg-Witten curve expression for the theory.

Abstract

We obtain Nekrasov-type expressions for the Seiberg-Witten prepotential for the six-dimensional (1,0) supersymmetric E-string theory compactified on T^2 with nontrivial Wilson lines. We consider compactification with four general Wilson line parameters, which partially break the E_8 global symmetry. In particular, we investigate in detail the cases where the Lie algebra of the unbroken global symmetry is E_n + A_{8-n} with n=8,7,6,5 or D_8. All our Nekrasov-type expressions can be viewed as special cases of the elliptic analogue of the Nekrasov partition function for the SU(N) gauge theory with N_f=2N flavors. We also present a new expression for the Seiberg-Witten curve for the E-string theory with four Wilson line parameters, clarifying the connection between the E-string theory and the SU(2) Seiberg-Witten theory with N_f=4 flavors.