Periods and Duality Symmetries in Calabi-Yau Compactifications

Abstract

We derive the period structure of several one-modulus Calabi-Yau manifolds. With this knowledge we then obtain the generators of the duality group and the mirror map that defines the physical variable $t$ representing the radius of compactification. We also describe the fundamental region of $t$ and discuss its relation with automorphic functions. As a byproduct of our analysis we compute the non-perturbative corrections of Yukawa couplings.

(37 pages, one figure not included)

References in corpus (6)

• Topological Field Theory and Rational Curves
• Picard-Fuchs equations and mirror maps for hypersurfaces
• Picard-Fuchs equations and mirror maps for hypersurfaces
• On the Solution of Topological Landau-Ginzburg Models with $c=3$
• Mirror Manifolds: A Brief Review and Progress Report
• Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians

Cited by in corpus (53)

• Exact Results for N=2 Compactifications of Heterotic Strings
• Holomorphic Anomalies in Topological Field Theories
• Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces
• Mirror Symmetry for Two Parameter Models -- II
• Stability of flux compactifications and the pattern of supersymmetry breaking
• On the Vacuum Structure of Type II String Compactifications on Calabi-Yau Spaces with H-Fluxes
• Mirror Symmetry for Two Parameter Models -- I
• Calabi-Yau Moduli Space, Mirror Manifolds and Spacetime Topology Change in String Theory
• Mirror Symmetry, Mirror Map and Applications to Complete Intersection Calabi-Yau Spaces
• On Gauge Couplings in String Theory
• Arithmetic and Attractors
• (0,2) Landau-Ginzburg Theory
• Mirror Manifolds in Higher Dimension
• Flux Compactifications on Calabi-Yau Threefolds
• Considerations of One-Modulus Calabi-Yau Compactifications: Picard-Fuchs Equations, Kähler Potentials and Mirror Maps
• Enumerating Flux Vacua with Enhanced Symmetries
• GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces
• The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces
• Magnetized E3-brane instantons in F-theory
• New Attractors and Area Codes
• Swampland Distance Conjecture for One-Parameter Calabi-Yau Threefolds
• Landau-Ginzburg String Vacua
• Picard-Fuchs Equations and Special Geometry
• Four-Dimensional Effective Supergravity and Soft Terms in M-Theory
• D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay
• Automorphic Forms and Fermion Masses
• Matrix factorisations and permutation branes
• Comment on the Generation Number in Orbifold Compactifications
• Periods for Calabi--Yau and Landau--Ginzburg Vacua
• D-branes on some one- and two-parameter Calabi-Yau hypersurfaces
• CP Symmetry and Symplectic Modular Invariance
• Holomorphic Couplings in String Theory
• Real Mirror Symmetry for One-parameter Hypersurfaces
• Landscaping with fluxes and the E8 Yukawa Point in F-theory
• Collapsing D-Branes in Calabi-Yau Moduli Space: I
• Mirror Symmetry and the Moduli Space for Generic Hypersurfaces in Toric Varieties
• A D-Brane Landscape on Calabi-Yau Manifolds
• Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings
• Rational curves on Calabi-Yau manifolds: verifying predictions of Mirror Symmetry
• D(-1)-Instanton Superpotential In String Theory
• Duality Group for Calabi-Yau 2-Moduli Space
• Some monodromy groups of finite index in $S{p}_4(\mathbb{Z})$
• Towards a complete mass spectrum of type-IIB flux vacua at large complex structure
• Topics in Cubic Special Geometry
• An analysis of soft terms in Calabi-Yau compactifications
• Recent Efforts in the Computation of String Couplings:
• Rational Curves on Calabi-Yau Threefolds
• Hemisphere Partition Function and Monodromy
• The Construction of Mirror Symmetry
• Mirror Symmetry of Calabi-Yau Manifolds and Flat Coordinates
• Instanton Corrected Non-Supersymmetric Attractors
• Two One-Parameter Special Geometries
• Can we distinguish SUSY breaking terms between weakly and strongly coupled heterotic string theories ?