2005/06/27 by Nick Halmagyi, Annamaria Sinkovics, Piotr Sulkowski
Physics and Astronomy · #Black Holes and Theoretical Physics #Quantum Mechanics and Non-Hermitian Physics #Topological Materials and Phenomena #hep-th
paper · pdf · doi:10.1088/1126-6708/2006/01/040
published as JHEP 0601 (2006) 040 · 39 pages, 8 figures
arxiv created 2005/06/27 · openalex publication_date 2006/01/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We show that Calabi-Yau crystals generate certain Chern-Simons knot invariants, with Lagrangian brane insertions generating the unknot and Hopf link invariants. Further, we make the connection of the crystal brane amplitudes to the topological vertex formulation explicit and show that the crystal naturally resums the corresponding topological vertex amplitudes. We also discuss the conifold and double wall crystal model in this context. The results suggest that the free energy associated to the crystal brane amplitudes can be simply expressed as a target space Gopakumar-Vafa expansion.