Open orbifold Gromov-Witten invariants of [ℂ3 /ℤn]: localization and mirror symmetry

Andrea Brini*, Renzo Cavalieri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of [ℂ3 /ℤn] and provide extensive checks with predictions from open string mirror symmetry. To this aim, we set up a computation of open string invariants in the spirit of Katz-Liu [23], defining them by localization. The orbifold is viewed as an open chart of a global quotient of the resolved conifold, and the Lagrangian as the fixed locus of an appropriate anti-holomorphic involution. We consider two main applications of the formalism. After warming up with the simpler example of [ℂ3 /ℤ3], where we verify physical predictions of Bouchard, Klemm, Mariño and Pasquetti [4,5], the main object of our study is the richer case of [ℂ3 /ℤ4], where two different choices are allowed for the Lagrangian. For one choice, we make numerical checks to confirm the B-model predictions; for the other, we prove a mirror theorem for orbifold disc invariants, match a large number of annulus invariants, and give mirror symmetry predictions for open string invariants of genus ≤ 2.

Original languageEnglish
Pages (from-to)879-933
Number of pages55
JournalSelecta Mathematica, New Series
Issue number4
Early online date27 May 2011
Publication statusPublished - 1 Dec 2011


  • D-branes
  • Gromov-Witten invariants
  • Mirror symmetry
  • Open strings
  • Orbifolds

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)


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