Knot invariants and Calabi-Yau crystals

Abstract

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.

arXiv comment39 pages, 8 figures

References in corpus (8)

• The Topological Vertex
• Topological Strings and Integrable Hierarchies
• Knot Invariants and Topological Strings
• Knots, links and branes at large N
• Polynomial invariants for torus knots and topological strings
• Derivation of Calabi-Yau Crystals from Chern-Simons Gauge Theory
• Chern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers
• Universal Correlators from Geometry

Cited by in corpus (13)

• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Topological strings, strips and quivers
• Donaldson-Thomas invariants, torus knots, and lattice paths
• Wall-crossing, free fermions and crystal melting
• Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's
• Crystal Model for the Closed Topological Vertex Geometry
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Non-compact Topological Branes on Conifold
• D-Brane Amplitudes in Topological String on Conifold
• Wall-crossing, open BPS counting and matrix models
• BPS states, crystals and matrices
• q-Deformed Oscillators and D-branes on Conifold
• Quantum mirror curve of periodic chain geometry