2010/07/31 by Andrea Brini, Renzo Cavalieri · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #hep-th #math-ph #math.AG #math.MP
paper · pdf · doi:10.1007/s00029-011-0060-4
44 pages + appendices; v2: exposition improved, misprints corrected, version to appear on Selecta Mathematica; v3: last minute mistake found and fixed for the symmetric brane setup of [C^3/Z_4]; in press
openalex publication_date 2011/05/26 · arxiv created 2011/06/13 · arxiv updated 2011/06/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
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, 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, Marino and Pasquetti, 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.