Landau-Ginzburg/Calabi-Yau correspondence for quintic three-folds via symplectic transformations
type: Item
instance of: scholarly article
title: Landau-Ginzburg/Calabi-Yau correspondence for quintic three-folds via symplectic transformations
zbMATH Open document ID: 1197.14043
author: Alessandro Chiodo
author: Yongbin Ruan
published in: Inventiones Mathematicae
publication date: 2010-09-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/0812.4660
review text: The authors show that the J-function encoding Fan-Jarvis-Ruan-Witten theory on the A-side equals via a mirror map to the I-function embodying the period integrals at the Gepner point on the B-side. This identification inscribes the physical Landau-Ginzburg Calabi-Yau correspondence within the enumerative geometry of moduli of curves and yields via Givental's quantization a prediction on the relation between the higher genus potential of the quintic threefold and that of Fan-Jarvis-Ruan-Witten theory.
reviewed by: Vehbi Emrah Paksoy
Mathematics Subject Classification ID: 14J33
Mathematics Subject Classification ID: 14N35
Mathematics Subject Classification ID: 53D45
zbMATH DE Number: 5782775
zbMATH Keywords: Landau-Ginzburg
zbMATH Keywords: Calabi-Yau
zbMATH Keywords: Fan-Jarvis-Ruan-Witten theory
zbMATH Keywords: quintic threefold
zbMATH Keywords: W-curves
MaRDI profile type: Publication
OpenAlex ID: W2047178258
arXiv ID: 0812.4660
cites work: Gromov-Witten theory of Deligne-Mumford stacks
cites work: Moduli of twisted spin curves
cites work: Compactifying the space of stable maps
cites work: A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory.
cites work: The Witten top Chern class via 𝐾-theory
cites work: Stable twisted curves and their \(r\)-spin structures
cites work: Towards an enumerative geometry of the moduli space of twisted curves and rth roots
cites work: Twisted \(r\)-spin potential and Givental's quantization
cites work: On the crepant resolution conjecture in the local case
cites work: Computing genus-zero twisted Gromov-Witten invariants
cites work: Wall-crossings in toric Gromov-Witten theory. I: Crepant examples
cites work: Quantum Riemann-Roch, Lefschetz and Serre
cites work: LG/CY correspondence: the state space isomorphism
cites work: Quantum cohomology and crepant resolutions: a conjecture
cites work: Tautological relations and the $r$-spin Witten conjecture
cites work: Geometry and analysis of spin equations
cites work: The Witten equation, mirror symmetry, and quantum singularity theory
cites work: Equivariant Gromov - Witten Invariants
cites work: A mirror theorem for toric complete intersections
cites work: Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions
cites work: Geometry of the moduli of higher spin curves.
cites work: Moduli spaces of higher spin curves and integrable hierarchies
cites work: An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
cites work: Intersection theory on the moduli space of curves and the matrix Airy function
cites work: Mirror principle. I
cites work: Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds
cites work: A topological view of Gromov-Witten theory
cites work: Q3409132
cites work: Algebraic construction of Witten's top Chern class
cites work: Q5465214
cites work: Q4012873
cites work: Q4288666
cites work: Phases of \(N=2\) theories in two dimensions
cites work: The reduced genus $1$ Gromov-Witten invariants of Calabi-Yau hypersurfaces
DOI: 10.1007/S00222-010-0260-0
description: scientific article