Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections

Abstract

We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2 quotients that lead to a new class of heterotic duals.

117 pages, 1 Postscript figure

References in corpus (76)

• Phases of $N=2$ Theories In Two Dimensions
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Massless Black Holes and Conifolds in String Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- I
• Black Hole Attractors and the Topological String
• The Topological Vertex
• Exact Results for N=2 Compactifications of Heterotic Strings
• Comments on String Dynamics in Six Dimensions
• Algebras, BPS States, and Strings
• Holomorphic Anomalies in Topological Field Theories
• Mirror Manifolds And Topological Field Theory
• Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces
• Automorphic forms with singularities on Grassmannians
• Mirror Symmetry for Two Parameter Models -- II
• Nonperturbative Results on the Point Particle Limit of N=2 Heterotic String Compactifications
• K3--Fibrations and Heterotic-Type II String Duality
• Mirror Symmetry for Two Parameter Models -- I
• Calabi-Yau fourfolds for M- and F-Theory compactifications
• Second-Quantized Mirror Symmetry
• Evidence for Heterotic/Heterotic Duality
• K3 Surfaces and String Duality
• Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
• A Generalized Construction of Mirror Manifolds
• c=1 String as the Topological Theory of the Conifold
• Mirror Symmetry, Mirror Map and Applications to Complete Intersection Calabi-Yau Spaces
• Matrix Model as a Mirror of Chern-Simons Theory
• Quantum Background Independence In String Theory
• Enhanced Gauge Symmetry in Type II String Theory
• On Gauge Couplings in String Theory
• Arithmetic and Attractors
• BPS States of Exceptional Non-Critical Strings
• PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
• D-branes on the Quintic
• BPS States, String Duality, and Nodal Curves on K3
• On the Ubiquity of K3 Fibrations in String Duality
• Counting higher genus curves in a Calabi-Yau manifold
• N=2 Type II- Heterotic duality and Higher derivative F-terms
• GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces
• Counting BPS Blackholes in Toroidal Type II String Theory
• All Loop Topological String Amplitudes From Chern-Simons Theory
• Dual String Pairs With N=1 And N=2 Supersymmetry In Four Dimensions
• Duality Between the Webs of Heterotic and Type II Vacua
• S-duality and Topological Strings
• Phases of Supersymmetric D-branes on Kaehler Manifolds and the McKay correspondence
• Dual Cones and Mirror Symmetry for Generalized Calabi-Yau Manifolds
• Aspects of Duality in N=2 String Vacua
• Strong Coupling Singularities and Non-abelian Gauge Symmetries in $N=2$ String Theory
• Mirror duality and string-theoretic Hodge numbers
• Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians
• Exact Gravitational Threshold Correction in the FHSV Model
• On the partition sum of the NS five-brane
• Calabi-Yau 4-folds and toric fibrations
• Generalized Calabi-Yau Manifolds and the Mirror of a Rigid Manifold
• The Monomial-Divisor Mirror Map
• Searching for K3 Fibrations
• A Stringy Test of the Fate of the Conifold
• Chiral Rings Do Not Suffice: N=(2,2) Theories with Nonzero Fundamental Group
• SU(4) Instantons on Calabi-Yau Threefolds with Z_2 x Z_2 Fundamental Group
• Mirror Maps and Instanton Sums for Complete Intersections in Weighted Projective Space
• Mirror Symmetry and the Moduli Space for Generic Hypersurfaces in Toric Varieties
• All Abelian Symmetries of Landau-Ginzburg Potentials
• Toric complete intersections and weighted projective space
• Torus-Fibered Calabi-Yau Threefolds with Non-Trivial Fundamental Group
• New Branches of String Compactifications and their F-Theory Duals
• String Duality and Modular Forms
• Resonant Hypergeometric Systems and Mirror Symmetry
• N=2 Type I-Heterotic Duality and Higher Derivative F-Terms
• String Amplitudes and N=2, d=4 Prepotential in Heterotic K3 x T^2 Compactifications
• The Deformation Space of Calabi-Yau n-folds with canonical singularities can be obstructed
• Counting Curves with Modular Forms
• Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds
• Product formulas for modular forms on O(2,n) (after R.Borcherds)
• ORBIFOLDS WITH DISCRETE TORSION AND MIRROR SYMMETRY
• Special Geometry and Automorphic Forms

Cited by in corpus (69)

• Split States, Entropy Enigmas, Holes and Halos
• Precision Counting of Small Black Holes
• Global F-theory GUTs
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• Direct Integration of the Topological String
• Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors
• F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds
• Holomorphic Anomaly in Gauge Theories and Matrix Models
• Exact and Asymptotic Degeneracies of Small Black Holes
• New Calabi-Yau Manifolds with Small Hodge Numbers
• Gromov-Witten theory and Noether-Lefschetz theory
• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Three-Family Particle Physics Models from Global F-theory Compactifications
• General U(1)xU(1) F-theory Compactifications and Beyond: Geometry of unHiggsings and novel Matter Structure
• Toric Construction of Global F-Theory GUTs
• Global SO(10) F-theory GUTs
• Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
• Landscaping with fluxes and the E8 Yukawa Point in F-theory
• Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry
• Counting BPS states on the Enriques Calabi-Yau
• Topological String Theory on Compact Calabi-Yau: Modularity and Boundary Conditions
• Refined swampland distance conjecture and exotic hybrid Calabi-Yaus
• Mathieu Moonshine and N=2 String Compactifications
• Black Holes and Large Order Quantum Geometry
• Calabi-Yau Threefolds With Small Hodge Numbers
• PALP - a User Manual
• Hodge Numbers for CICYs with Symmetries of Order Divisible by 4
• Lectures on Mirror Symmetry and Topological String Theory
• Direct integration for general Omega backgrounds
• Curve counting on elliptic Calabi-Yau threefolds via derived categories
• Black Hole Meiosis
• Heterotic-Type IIA Duality and Degenerations of K3 Surfaces
• Deforming, revolving and resolving - New paths in the string theory landscape
• Quantum geometry of elliptic Calabi-Yau manifolds
• The elliptic genus from split flows and Donaldson-Thomas invariants
• Topological Amplitudes in Heterotic Strings with Wilson Lines
• Modular Curves and the Refined Distance Conjecture
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Landscape Study of Target Space Duality of (0,2) Heterotic String Models
• Conway Subgroup Symmetric Compactifications Of Heterotic String
• Borcherds Algebras and N=4 Topological Amplitudes
• Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings
• Noether-Lefschetz theory and the Yau-Zaslow conjecture
• The 14th case VHS via K3 fibrations
• Triadophilia: A Special Corner in the Landscape
• A pair of Calabi-Yau manifolds from a two parameter non-Abelian gauged linear sigma model
• Topological Strings on Elliptic Fibrations
• Wall Crossing Phenomenology of Orientifolds
• Modular Forms as Classification Invariants of 4D N=2 Heterotic--IIA Dual Vacua
• Scaling Black Holes and Modularity
• Partial SUSY Breaking for Asymmetric Gepner Models and Non-geometric Flux Vacua
• Solving the Topological String on K3 Fibrations
• The Spectra of Supersymmetric States in String Theory
• On genus one fibered Calabi-Yau threefolds with 5-sections
• Heterotic flux backgrounds and their IIA duals
• The Ruled Vertex and D-E Degenerations
• Jacobi Forms of Higher Index and Paramodular Groups in N=2, D=4 Compactifications of String Theory
• The making of Calabi-Yau spaces: Beyond toric hypersurfaces
• Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions
• Heterotic strings on $(K3\times T^2)/{\mathbb{Z}}_3$ and their dual Calabi-Yau threefolds
• The Weak Gravity Conjecture and BPS Particles
• Target Space Dualities of Heterotic Grand Unified Theories
• Max Kreuzer's Contributions to the Study of Calabi-Yau Manifolds
• Topological String on elliptic CY 3-folds and the ring of Jacobi forms
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM
• Effective Superpotentials of Type II D-brane/F-theory on Compact Complete Intersection Calabi-Yau Threefolds
• On Real Intrinsic Wall Crossings
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• Direct Computation of Monodromy Matrices and Classification of 4d N=2 Heterotic--IIA Dual Vacua