Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry

Abstract

We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of [C^3/Z_n], 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 [C^3/Z_3], where we verify physical predictions of Bouchard, Klemm, Marino and Pasquetti, the main object of our study is the richer case of [C^3/Z_4], 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 \leq 2.

arXiv comment44 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

References in corpus (2)

• Open string amplitudes and large order behavior in topological string theory
• Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc

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• Symplectic cuts and open/closed strings I
• Symplectic cuts and open/closed strings II
• Dubrovin duality and mirror symmetry for ADE resolutions
• A Gamma Class Formula for Open Gromov-Witten Calculations
• Enumerative geometry of surfaces and topological strings
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