D-branes as a Bubbling Calabi-Yau

Abstract

We prove that the open topological string partition function on a D-brane configuration in a Calabi-Yau manifold X takes the form of a closed topological string partition function on a different Calabi-Yau manifold X_b. This identification shows that the physics of D-branes in an arbitrary background X of topological string theory can be described either by open+closed string theory in X or by closed string theory in X_b. The physical interpretation of the ''bubbling'' Calabi-Yau X_b is as the space obtained by letting the D-branes in X undergo a geometric transition. This implies, in particular, that the partition function of closed topological string theory on certain bubbling Calabi-Yau manifolds are invariants of knots in the three-sphere.

32 pages; v.2 reference added

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• Spectral curves, emergent geometry, and bubbling solutions for Wilson loops
• Topological Holography: The Example of The D2-D4 Brane System
• A prediction for bubbling geometries
• Bubbling Calabi-Yau geometry from matrix models
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Macdonald topological vertices and brane condensates
• Topological Quiver Matrix Models and Quantum Foam
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• Two-Point Functions in ABJM Matrix Model
• Wall-crossing, open BPS counting and matrix models
• Surface Operators from M-strings
• Instanton Counting and Matrix Model
• Mirror of the refined topological vertex from a matrix model
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• Topological string entanglement
• Geometric transition in Non-perturbative Topological string
• BPS states, crystals and matrices
• BIons in topological string theory