On the Duality between the Heterotic String and F-Theory in 8 Dimensions

Abstract

In this note we compare the moduli spaces of the heterotic string compactified on a two-torus and F-Theory compactified on an elliptic K3 surface for the case of an unbroken E8 x E8 gauge group. The explicit map relating the deformation parameters alpha and beta of the F-Theory K3 surface to the moduli T and U of the heterotic torus is found using the close relationship between the K3 discriminant and the discriminant of the Calabi-Yau-threefold X(1,1,2,8,12)[24] in the limit of a large base P1.

10 pages, LaTeX

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Cited by in corpus (32)

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• Point-like Instantons on K3 Orbifolds
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• Geometric constraints in dual F-theory and heterotic string compactifications
• Exploring the landscape of heterotic strings on T^d
• The twelve dimensional super (2+2)-brane
• Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds
• The Cremmer-Scherk Mechanism in F-theory Compactifications on K3 Manifolds
• Heterotic T-fects, 6D SCFTs, and F-Theory
• Type I' and Real Algebraic Geometry
• Unwinding strings in semi-flatland
• Mathematics Underlying the F-Theory/Heterotic String Duality in Eight Dimensions
• Non-Geometric F-Theory-Heterotic Duality
• Ubiquity of non-geometry in heterotic compactifications
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• D=6, N=1 String Vacua and Duality
• U-folds as K3 fibrations
• Type IIB Flux Vacua from M-theory via F-theory
• F-theory and Heterotic Duality, Weierstrass Models from Wilson lines
• Map of Heterotic and Type IIB Moduli in 8 Dimensions
• Heterotic-Type II duality in the hypermultiplet sector
• Non-Geometric Vacua of the $\text{Spin}(32)/{\mathbb{Z}}_2$ Heterotic String and Little String Theories
• Affine Algebras at Infinite Distance Limits in the Heterotic String
• K3 metrics from little string theory
• Heterotic String Compactification and New Vector Bundles
• N=1 Dual String Pairs and their Modular Superpotentials
• Prepotential, Mirror Map and F-Theory on K3
• F-Theories on Double Sextics and Effective String Theories
• On K3 Surfaces with Large Complex Structure
• Modular Invariants for Lattice Polarized K3 Surfaces