Derivation of Calabi-Yau Crystals from Chern-Simons Gauge Theory

2004/09/30 by Takuya Okuda · 6 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1088/1126-6708/2005/03/047

published as JHEP0503:047,2005 · 18 pages, 5 figures; v.2 typos corrected, references added; v.3 minor typos corrected, a confusing expression modified

openalex publication_date 2005/03/18 · arxiv created 2007/02/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We derive new crystal melting models from Chern-Simons theory on the three-sphere. Via large N duality, these models compute amplitudes for A-model on the resolved conifold. The crystal is bounded by two walls whose distance corresponds to the Kahler modulus of the geometry. An interesting phenomenon is found where the Kahler modulus is shifted by the presence of non-compact D-branes. We also discuss the idea of using the crystal models as means of proving more general large N dualities to all order in g_s.

Citations

• Curve counting and instanton counting
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• D-branes as Defects in the Calabi-Yau Crystal
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs

Cited by

• Instantons on ALE spaces and orbifold partitions
• Crystal model for the closed topological vertex geometry
• Non-compact topological branes on conifold
• q-deformed oscillators and D-branes on conifold
• Knot invariants and Calabi-Yau crystals
• Oscillatory matrix model in Chern-Simons theory and Jacobi-theta determinantal point process