Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau threefolds

Abstract

We solve Bershadsky-Cecotti-Ooguri-Vafa (BCOV) holomorphic anomaly equation to determine the higher genus Gromov-Witten invariants ($g\le 5$) of the derived equivalent Calabi-Yau threefolds, which are of the appropriate codimensions in the Grassmannian Gr(2,7) and the Pfaffian Pf(7).

arXiv comment24 pages; minor corrections and references added (ver2); references added (ver3)

References in corpus (8)

• Massless Black Holes and Conifolds in String Theory
• Black Hole Attractors and the Topological String
• Arithmetic Properties of Mirror Map and Quantum Coupling
• Homological projective duality for Grassmannians of lines
• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Relative Lefschetz Action and BPS State Counting
• Topological wave functions and heat equations
• The Analogue of the Dedekind Eta Function for CY Manifolds I

Cited by in corpus (11)

• Integrability of the holomorphic anomaly equations
• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• Open mirror symmetry for Pfaffian Calabi-Yau 3-folds
• On solutions to Walcher's extended holomorphic anomaly equation
• Minuscule Schubert Varieties and Mirror Symmetry
• Movable vs Monodromy Nilpotent Cones of Calabi-Yau Manifolds
• BCOV ring and holomorphic anomaly equation
• Mirror symmetry and projective geometry of Reye congruences I
• Nonabelian mirrors and Gromov-Witten invariants
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM
• Pfaffian Calabi-Yau Threefolds and Mirror Symmetry