Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model
arXiv:0903.2092 · doi:10.1016/j.nuclphysb.2009.04.010
Abstract
We study topological strings on local toric del Pezzo surfaces by a method called remodeling the B-model which was recently proposed by Bouchard, Klemm, Marino and Pasquetti. For a large class of local toric del Pezzo surfaces we prove a functional formula of the Bergman kernel which is the basic constituent of the topological string amplitudes by the topological recursion relation of Eynard and Orantin. Because this formula is written as a functional of the period, we can obtain the topological string amplitudes at any point of the moduli space by a simple change of variables of the Picard-Fuchs equations for the period. By this formula and mirror symmetry we compute the A-model amplitudes on K_{F_2}, and predict the open orbifold Gromov-Witten invariants of C^3/Z_4.
31 pages, 4 figures. v2: an example in Subsection 4.3 added, a footnote in Subsection 4.4 added, minor errors in Appendix E corrected, a reference added. v3: typos corrected
References in corpus (12)
- Open string amplitudes and large order behavior in topological string theory
- Remodeling the B-model
- Les Houches lectures on matrix models and topological strings
- Integrability of the holomorphic anomaly equations
- Holomorphic anomaly and matrix models
- Holomorphic Anomaly in Gauge Theories and Matrix Models
- Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
- Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
- Two Dimensional Kodaira-Spencer Theory and Three Dimensional Chern-Simons Gravity
- Global Properties of Topological String Amplitudes and Orbifold Invariants
- Topological Strings and (Almost) Modular Forms
- Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples