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Exceptional String: Instanton Expansions and Seiberg-Witten Curve

Kenji Mohri

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.

Exceptional String: Instanton Expansions and Seiberg-Witten Curve

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.

Paper Structure

This paper contains 69 sections, 217 equations, 1 table.

Table of Contents

  1. Introduction
  2. E-String
  3. Homology lattice and affine root lattice
  4. Partition functions
  5. Four Torus Models
  6. Periods of elliptic curves
  7. Modular identities
  8. Model Building of E-Strings
  9. Principal series
  10. $\boldsymbol{E}_0$ and $\boldsymbol{E}_{\tilde{1}}$ models
  11. Kähler classes
  12. Periods
  13. Relation to Seiberg--Witten periods
  14. Genus Zero Partition Functions
  15. Recursion relations
  16. ...and 54 more sections