Localized mirror functor constructed from a Lagrangian torus

Cheol Hyun Cho, Hansol Hong, Siu Cheong Lau

Research output: Contribution to journalArticle

Abstract

Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold X, we define a holomorphic function W known as the Floer potential. We construct a canonical A-functor from the Fukaya category of X to the category of matrix factorizations of W. It provides a unified way to construct matrix factorizations from Lagrangian Floer theory. The technique is applied to toric Fano manifolds to transform Lagrangian branes to matrix factorizations and prove homological mirror symmetry. Using the method, we also obtain an explicit expression of the matrix factorization mirror to the real locus of the complex projective space.

Original languageEnglish
Pages (from-to)284-320
Number of pages37
JournalJournal of Geometry and Physics
Volume136
DOIs
Publication statusPublished - 2019 Feb

Fingerprint

Matrix Factorization
factorization
Functor
Factorization of Matrices
Mirror
Torus
mirrors
matrices
Fano Manifolds
Mirror Symmetry
Complex Projective Space
Symplectic Manifold
Branes
Locus
Analytic function
loci
fixing
Transform
symmetry

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Cite this

Cho, Cheol Hyun ; Hong, Hansol ; Lau, Siu Cheong. / Localized mirror functor constructed from a Lagrangian torus. In: Journal of Geometry and Physics. 2019 ; Vol. 136. pp. 284-320.
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Localized mirror functor constructed from a Lagrangian torus. / Cho, Cheol Hyun; Hong, Hansol; Lau, Siu Cheong.

In: Journal of Geometry and Physics, Vol. 136, 02.2019, p. 284-320.

Research output: Contribution to journalArticle

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