Examples of matrix factorizations from SYZ

Cheol Hyun Cho, Hansol Hong, Sangwook Lee

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We find matrix factorization corresponding to an anti-diagonal in ℂP1×ℂP1, and circle fibers in weighted projective lines using the idea of Chan and Leung of Strominger-Yau-Zaslow transformations. For the tear drop orbifolds, we apply this idea to find matrix factorizations for two types of potential, the usual Hori-Vafa potential or the bulk deformed (orbi)-potential. We also show that the direct sum of anti-diagonal with its shift, is equivalent to the direct sum of central torus fibers with holonomy (1,-1) and (-1,1) in the Fukaya category of ℂP1×ℂP1, which was predicted by Kapustin and Li from B-model calculations.

Original languageEnglish
Article number053
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume8
DOIs
Publication statusPublished - 2012 Aug 16

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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