F-theory and Heterotic Duality, Weierstrass Models from Wilson lines
arXiv:1910.12844 · doi:10.1140/epjc/s10052-020-08467-w
Abstract
We present how to construct elliptically fibered K3 surfaces via Weierstrass models which can be parametrized in terms of Wilson lines in the dual heterotic string theory. We work with a subset of reflexive polyhedras that admit two fibers whose moduli spaces contain the ones of the or heterotic theory compactified on a two torus without Wilson lines. One can then interpret the additional moduli as a particular Wilson line content in the heterotic strings. A convenient way to find such polytopes is to use graphs of polytopes where links are related to inclusion relations of moduli spaces of different fibers. We are then able to map monomials in the defining equations of particular K3 surfaces to Wilson line moduli in the dual theories. Graphs were constructed developing three different programs which give the gauge group for a generic point in the moduli space, the Weierstrass model as well as basic enhancements of the gauge group obtained by sending coefficients of the hypersurface equation defining the K3 surface to zero.
arXiv comment24 pages
References in corpus (28)
- Evidence for F-Theory
- Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
- Compactifications of F-Theory on Calabi--Yau Threefolds -- II
- Compactifications of F-Theory on Calabi--Yau Threefolds -- I
- K3 Surfaces and String Duality
- F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
- PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
- Measurement and QCD analysis of double-differential inclusive jet cross-sections in pp collisions at sqrt(s) = 8 TeV and ratios to 2.76 and 7 TeV
- Duality Between the Webs of Heterotic and Type II Vacua
- Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
- Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors
- Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
- Periods for Calabi--Yau and Landau--Ginzburg Vacua
- K3 surfaces, modular forms, and non-geometric heterotic compactifications
- On the Duality between the Heterotic String and F-Theory in 8 Dimensions
- A new twist on heterotic string compactifications
- F-theory, SO(32) and Toric Geometry
- Enhanced Gauge Symmetry in Type II and F-Theory Compactifications: Dynkin Diagrams from Polyhedra
- Type IIB flux vacua from G-theory II
- Discrete Symmetries in Heterotic/F-theory Duality and Mirror Symmetry
- PALP - a User Manual
- Towards Exotic Matter and Discrete Non-Abelian Symmetries in F-theory
- Type IIB flux vacua from G-theory I
- Elliptic Surfaces
- Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
- String Dualities and Toric Geometry: An Introduction
- TASI Lectures on Abelian and Discrete Symmetries in F-theory
- Mirror Symmetry in Physics: The Basics