Mirror Symmetry for Two Parameter Models -- II
arXiv:hep-th/9403187 · doi:10.1016/0550-3213(94)90155-4
Abstract
We describe in detail the space of the two Kähler parameters of the Calabi--Yau manifold by exploiting mirror symmetry. The large complex structure limit of the mirror, which corresponds to the classical large radius limit, is found by studying the monodromy of the periods about the discriminant locus, the boundary of the moduli space corresponding to singular Calabi--Yau manifolds. A symplectic basis of periods is found and the action of the generators of the modular group is determined. From the mirror map we compute the instanton expansion of the Yukawa couplings and the generalized index, arriving at the numbers of instantons of genus zero and genus one of each degree. We also investigate an symmetry that acts on a boundary of the moduli space.
57 pages + 9 figures using epsf
References in corpus (20)
- Phases of Theories In Two Dimensions
- Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
- Holomorphic Anomalies in Topological Field Theories
- Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces
- Mirror Symmetry for Two Parameter Models -- II
- Mirror Symmetry for Two Parameter Models -- I
- Calabi-Yau Moduli Space, Mirror Manifolds and Spacetime Topology Change in String Theory
- Topological Field Theory and Rational Curves
- Considerations of One-Modulus Calabi-Yau Compactifications: Picard-Fuchs Equations, Kähler Potentials and Mirror Maps
- Compactifications of moduli spaces inspired by mirror symmetry
- Multiple Mirror Manifolds and Topology Change in String Theory
- Picard-Fuchs equations and mirror maps for hypersurfaces
- Periods and Duality Symmetries in Calabi-Yau Compactifications
- Picard-Fuchs Equations and Special Geometry
- The Monomial-Divisor Mirror Map
- Mirror Maps and Instanton Sums for Complete Intersections in Weighted Projective Space
- Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings
- Rational curves on Calabi-Yau manifolds: verifying predictions of Mirror Symmetry
- Duality Group for Calabi-Yau 2-Moduli Space
- Rational Curves on Calabi-Yau Threefolds
Cited by in corpus (211)
- Exact Results for N=2 Compactifications of Heterotic Strings
- Large-Volume Flux Compactifications: Moduli Spectrum and D3/D7 Soft Supersymmetry Breaking
- Algebras, BPS States, and Strings
- Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces
- Two-Dimensional Black Hole and Singularities of CY Manifolds
- Mirror Symmetry for Two Parameter Models -- II
- Building a Better Racetrack
- Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
- Infinite Distances in Field Space and Massless Towers of States
- Elliptic genera of 2d N=2 gauge theories
- On the Vacuum Structure of Type II String Compactifications on Calabi-Yau Spaces with H-Fluxes
- Mirror Symmetry, Mirror Map and Applications to Complete Intersection Calabi-Yau Spaces
- Open string instantons and superpotentials
- On Gauge Couplings in String Theory
- Arithmetic and Attractors
- Jumping Through Loops: On Soft Terms from Large Volume Compactifications
- Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory
- Infinite Distance Networks in Field Space and Charge Orbits
- Flux Compactifications on Calabi-Yau Threefolds
- The Swampland Distance Conjecture for Kahler moduli
- Backreacted Axion Field Ranges in String Theory
- On the Ubiquity of K3 Fibrations in String Duality
- Counting higher genus curves in a Calabi-Yau manifold
- Measuring Small Distances in N=2 Sigma Models
- GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces
- On the Explicit Construction and Statistics of Calabi-Yau Flux Vacua
- D-branes, open string vertex operators, and Ext groups
- Vacua with Small Flux Superpotential
- Orientifolds of Gepner Models
- Inflating in a Better Racetrack
- Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
- The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces
- Hypergeometric functions and mirror symmetry in toric varieties
- Building an explicit de Sitter
- Strings of Minimal 6d SCFTs
- Mirror symmetry for open strings
- Black hole bound states in AdS_3 x S^2
- Compactification of Type IIB String Theory on Calabi-Yau Threefolds
- Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
- On the Classification of Reflexive Polyhedra
- Small Cosmological Constants in String Theory
- Les Houches Lectures on Strings and Arithmetic
- D-branes on Stringy Calabi-Yau Manifolds
- Sequestering in String Theory
- Computing Brane and Flux Superpotentials in F-theory Compactifications
- Non-Perturbative Superpotentials in F-theory and String Duality
- D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay
- Resolution of Orbifold Singularities in String Theory
- Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and Extensions of Landau Ginzburg Theory
- Matrix factorisations and permutation branes
- The Ubiquitous Throat
- Local string models of soft supersymmetry breaking
- Heterotic Moduli Stabilisation
- A New Construction of Calabi-Yau Manifolds: Generalized CICYs
- D-branes on some one- and two-parameter Calabi-Yau hypersurfaces
- D-Branes on K3-Fibrations
- Finding all flux vacua in an explicit example
- Attractors and Arithmetic
- Modular Symmetries and the Swampland Conjectures
- Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications
- Holomorphic Couplings in String Theory
- Quantum cohomology of partial flag manifolds
- A Stringy Test of the Fate of the Conifold
- Half-Twisted Correlators from the Coulomb Branch
- Notes on certain other (0,2) correlation functions
- D-Branes and Bundles on Elliptic Fibrations
- EFT strings and emergence
- Exact Monodromy Group of N=2 Heterotic Superstring
- Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces
- Effective superpotentials for compact D5-brane Calabi-Yau geometries
- Chiral Rings Do Not Suffice: N=(2,2) Theories with Nonzero Fundamental Group
- New Methods for Characterizing Phases of 2D Supersymmetric Gauge Theories
- Non-Critical Strings, Del Pezzo Singularities And Seiberg-Witten Curves
- Swampland Constraints on 5d Supergravity
- Moduli Stabilisation and Applications in IIB String Theory
- Landscaping with fluxes and the E8 Yukawa Point in F-theory
- Moduli Stabilization in Asymptotic Flux Compactifications
- Massless D-Branes on Calabi-Yau Threefolds and Monodromy
- Collapsing D-Branes in Calabi-Yau Moduli Space: I
- Relative periods and open-string integer invariants for a compact Calabi-Yau hypersurface
- Small Flux Superpotentials for Type IIB Flux Vacua Close to a Conifold
- Moduli Stabilization, Large-Volume dS Minimum Without anti-D3-Branes, (Non-)Supersymmetric Black Hole Attractors and Two-Parameter Swiss Cheese Calabi-Yau's
- Large Volume Axionic Swiss-Cheese Inflation
- Calculations for Mirror Symmetry with D-branes
- Mirror Symmetry and the Moduli Space for Generic Hypersurfaces in Toric Varieties
- Critical Points and Phase Transitions in 5D Compactifications of M-Theory
- Low Energy Supersymmetry from Non-Geometry
- Multiple Mellin-Barnes Integrals as Periods of Calabi-Yau Manifolds With Several Moduli
- Flop Transitions in M-theory Cosmology
- Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau
- Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry
- Instanton Numbers and Exchange Symmetries in Dual String Pairs
- Fibrewise T-Duality for D-Branes on Elliptic Calabi-Yau
- The Landau-Ginzburg to Calabi-Yau Dictionary for D-Branes
- (0,2) Elephants
- Dynamical Topology Change in M Theory
- Type IIB flux vacua from G-theory II
- Flux Vacua Statistics for Two-Parameter Calabi-Yau's
- Accidental Inflation in the Landscape
- Scanning the Landscape of Flux Compactifications: Vacuum Structure and Soft Supersymmetry Breaking
- Mirror Symmetry and the Type II String
- On the modified KKLT procedure: a case study for the P_{11169}[18] model
- Some Navigation Rules for D-Brane Monodromy
- Mirror Principle II
- Type IIB flux vacua from G-theory I
- Two-Sphere Partition Functions and Gromov-Witten Invariants
- Enhanced Symmetries in Multiparameter Flux Vacua
- Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings
- Solitons in Seiberg-Witten Theory and D-branes in the Derived Category
- Categories of Massless D-Branes and del Pezzo Surfaces
- 4d strings at strong coupling
- Deformations of Toric Varieties via Minkowski Sum Decompositions of Polyhedral Complexes
- Some remarks on defects and T-duality
- On Instanton Superpotentials, Calabi-Yau Geometry, and Fibrations
- A-Model Correlators from the Coulomb Branch
- Supersymmetric Rényi Entropy in Two Dimensions
- Global embeddings for branes at toric singularities
- The Moduli Space of N = 2 Superconformal Field Theories
- The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
- Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds
- Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
- Supersymmetric Flux Compactifications and Calabi-Yau Modularity
- Fourier Mukai Transforms and Applications to String Theory
- Duality Group for Calabi-Yau 2-Moduli Space
- Sequestered Dark Matter
- The Spectra of Type IIB Flux Compactifications at Large Complex Structure
- Quantum K-Theory of Calabi-Yau Manifolds
- Counting Curves with Modular Forms
- Black String Entropy and Fourier-Mukai Transform
- Quantum geometry of elliptic Calabi-Yau manifolds
- Modularity from Monodromy
- Ample D4-D2-D0 Decay
- Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
- String Duality and Enumeration of Curves by Jacobi Forms
- Swiss Cheese D3-D7 Soft SUSY Breaking
- D-brane central charge and Landau-Ginzburg orbifolds
- A Note on the String Analog of Super-Symmetric Yang-Mills
- Detection of Low Tension Cosmic Superstrings
- Rigid Limit in N=2 Supergravity and Weak-Gravity Conjecture
- A Note on Computations of D-brane Superpotential
- Challenges for D-brane large-field inflation with stabilizer fields
- Systematics of perturbatively flat flux vacua
- Towards a complete mass spectrum of type-IIB flux vacua at large complex structure
- Deformations of Calabi-Yau hypersurfaces arising from deformations of toric varieties
- Excision of Singularities by Stringy Domain Walls
- Special geometry on the 101 dimesional moduli space of the quintic threefold
- Exact computation of the Special geometry for Calabi-Yau hypersurfaces of Fermat type
- The Geometry of Gauged Linear Sigma Model Correlation Functions
- Universal Class of Type-IIB Flux Vacua with Analytic Mass Spectrum
- Light Strings and Strong Coupling in F-theory
- An analysis of soft terms in Calabi-Yau compactifications
- Where is the large radius limit?
- On the Search for Low
- Mirror Symmetry Constructions: A Review
- Flux Modularity, F-Theory, and Rational Models
- Matrix Factorizations, Massey Products and F-Terms for Two-Parameter Calabi-Yau Hypersurfaces
- Analytics of type IIB flux vacua and their mass spectra
- Classifying divisor topologies for string phenomenology
- Gromov-Witten invariants and localization
- Holomorphic Couplings In Non-Perturbative String Compactifications
- A pair of Calabi-Yau manifolds from a two parameter non-Abelian gauged linear sigma model
- Analytic Periods via Twisted Symmetric Squares
- Topological Strings on Elliptic Fibrations
- Seeking de-Sitter Vacua in the String Landscape
- Rational curves on Calabi-Yau threefolds
- On the structure of supersymmetric T3 fibrations
- On K3 Correspondences
- Type IIB Flux Vacua at Large Complex Structure
- Prepotentials, Bi-linear Forms on Periods and Enhanced Gauge Symmetries in Type-II Strings
- The Ruled Vertex and D-E Degenerations
- The Breakdown of Topology at Small Scales
- Calabi-Yau threefolds with a curve of singularities and counterexamples to the Torelli problem
- On genus one fibered Calabi-Yau threefolds with 5-sections
- Heterotic flux backgrounds and their IIA duals
- Rational Curves on Calabi-Yau Threefolds
- Hemisphere Partition Function and Monodromy
- Finding the Mirror of the Beauville Manifold
- Gromov-Witten Invariants via Algebraic Geometry
- Probing Geometry with Stability Conditions
- Axion species scale and axion weak gravity conjecture-like bound
- Large N dualities and transitions in geometry
- A Note on of Divisors of CY Fourfolds I
- A Healthy Electron/Neutron EDM in D3/D7 mu-Split-Like SUSY
- Conjectures on (0,2) Mirror Symmetry
- Special Geometry and Automorphic Forms
- Bagger-Witten line bundles on moduli spaces of elliptic curves
- On D0-branes in Gepner models
- Mirror Symmetry of Calabi-Yau Manifolds and Flat Coordinates
- Non Perturbative Check of N=2, D=4 Heterotic/Type II Duality
- On Natural Inflation and Moduli Stabilisation in String Theory
- Mirror Symmetry and Discriminants
- Instanton Corrected Non-Supersymmetric Attractors
- Mirror Symmetry, D-brane Superpotential and Ooguri-Vafa Invariants of Compact Calabi-Yau Manifolds
- String Loop Moduli Stabilisation and Cosmology in IIB Flux Compactifications
- Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
- Aspects of Collapsing Cycles
- Conformal bootstrap and Mirror symmetry of states in Gepner models
- Embedding of Calabi-Yau deformations into toric varieties
- Large N Duality for Compact Calabi-Yau Threefolds
- Stable Sheaves Over K3 Fibrations
- Topological String on elliptic CY 3-folds and the ring of Jacobi forms
- Analytic equivalence of geometric transitions
- Recent Developments in Topological String Theory
- Topics in Supergravity Phenomenology
- Symplectic capacities of toric manifolds and related results
- Gaugings and other aspects in supergravity
- Gromov-Witten Theory and Threshold Corrections
- Some finiteness results for Calabi-Yau threefolds
- Exoflops in Two Dimensions
- Local Mirror Symmetry and Type IIA Monodromy of Calabi-Yau manifolds
- A Database of Calabi-Yau Orientifolds and the Size of D3-Tadpoles