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

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 $g_s$.

18 pages, 5 figures; v.2 typos corrected, references added; v.3 minor typos corrected, a confusing expression modified

References in corpus (6)

• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Brownian Motion, Chern-Simons Theory, and 2d Yang-Mills
• Curve counting and instanton counting
• Chern-Simons Theory in Lens Spaces from 2d Yang-Mills on the Cylinder
• D-branes as Defects in the Calabi-Yau Crystal
• Chern-Simons matrix model for local conifold

Cited by in corpus (40)

• Les Houches lectures on matrix models and topological strings
• Crystal Melting and Toric Calabi-Yau Manifolds
• Refined Topological Vertex, Cylindric Partitions and the U(1) Adjoint Theory
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Instantons on ALE spaces and orbifold partitions
• Discrete and oscillatory Matrix Models in Chern-Simons theory
• Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory
• Chern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers
• Deformed boson-fermion correspondence, Q-bosons, and topological strings on the conifold
• Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's
• Wall Crossing As Seen By Matrix Models
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• The Volume Conjecture and Topological Strings
• Crystal Model for the Closed Topological Vertex Geometry
• Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• A Note on Knot Invariants and q-Deformed 2d Yang-Mills
• Knot invariants and Calabi-Yau crystals
• From effective actions to the background geometry
• Non-compact Topological Branes on Conifold
• D-Brane Amplitudes in Topological String on Conifold
• Intersecting Defects and Supergroup Gauge Theory
• Unitary Chern-Simons matrix model and the Villain lattice action
• Crystals and intersecting branes
• Oscillatory matrix model in Chern-Simons theory and Jacobi-theta determinantal point process
• Chern-Simons Theory on Seifert Manifold and Matrix Model
• Emergent Phase Space Description of Unitary Matrix Model
• Torus knot polynomials and susy Wilson loops
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• Toric Geometry and String Theory
• Chern-Simons theory encoded on a spin chain
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Generalized Ablowitz-Ladik hierarchy in topological string theory
• Quantum mirror curve of periodic chain geometry
• New phase in Chern-Simons theory on lens space
• q-Deformed Oscillators and D-branes on Conifold
• Geometry and Combinatorics of Crystal Melting
• Periodic Schur Process, Cylindric Partitions and N=2* Theory
• Toward the construction of the general multi-cut solutions in Chern-Simons Matrix Models
• BIons in topological string theory