Exceptional String: Instanton Expansions and Seiberg-Witten Curve

TL;DR

This paper explores instanton expansions of E-string models using mirror symmetry and modular forms, and introduces a method to derive Seiberg-Witten curves with arbitrary Wilson lines via elliptic functions.

Contribution

It presents a novel approach to compute Seiberg-Witten curves for E-string theories with arbitrary Wilson lines using elliptic functions.

Findings

Explicit instanton expansion formulas for E-string models

A new method to derive Seiberg-Witten curves with Wilson lines

Enhanced understanding of the modular properties of E-string partition functions

Abstract

We investigate instanton expansions of partition functions of several toric E-string models using local mirror symmetry and elliptic modular forms. We also develop a method to obtain the Seiberg--Witten curve of E-string with arbitrary Wilson lines with the help of elliptic functions.