2009/02/04 by Daniel Krefl, Krefl, Daniel, Johannes Walcher +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.0902.0616
openalex publication_date 2009/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.