The Real Topological String on a local Calabi-Yau
arXiv:0902.0616
Abstract
We study the topological string on local P2 with O-plane and D-brane at its real locus, using three complementary techniques. In the A-model, we refine localization on the moduli space of maps with respect to the torus action preserved by the anti-holomorphic involution. This leads to a computation of open and unoriented Gromov-Witten invariants that can be applied to any toric Calabi-Yau with involution. We then show that the full topological string amplitudes can be reproduced within the topological vertex formalism. We obtain the real topological vertex with trivial fixed leg. Finally, we verify that the same results derive in the B-model from the extended holomorphic anomaly equation, together with appropriate boundary conditions. The expansion at the conifold exhibits a gap structure that belongs to a so far unidentified universality class.
37 pages, 4 figures
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- Non-Perturbative Quantum Geometry III
- Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry
- Orientifolds and the Refined Topological String
- Non-perturbative effects and wall-crossing from topological strings
- The Real Topological Vertex at Work
- A Note on Computations of D-brane Superpotential
- Wall Crossing Phenomenology of Orientifolds
- Towards a gauge theory interpretation of the real topological string
- Open/Closed Topological CP1 Sigma Model Revisited
- Real topological string amplitudes
- Topics in Open Topological Strings