A Vertex Formalism for Local Ruled Surfaces

Abstract

We develop a vertex formalism for topological string amplitudes on ruled surfaces with an arbitrary number of reducible fibers embedded in a Calabi-Yau threefold. Our construction is based on large N duality and localization with respect to a degenerate torus action. We also discuss potential generalizations of our formalism to a broader class of Calabi-Yau threefolds using the same underlying principles.

arXiv comment24 pages, 12 figures; v2: minor changes; v3: explanations added, results unchanged

References in corpus (10)

• Black Hole Attractors and the Topological String
• The Topological Vertex
• Topological Strings and Integrable Hierarchies
• Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings
• Enhanced Gauge Symmetry in Type II String Theory
• All Loop Topological String Amplitudes From Chern-Simons Theory
• Hodge integrals and invariants of the unknot
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Cited by in corpus (9)

• Topological strings and 5d T_N partition functions
• 5d/6d DE instantons from trivalent gluing of web diagrams
• Exact partition functions of Higgsed 5d $T_N$ theories
• Topological vertex formalism with O5-plane
• Topological string amplitudes for the local half K3 surface
• Introduction to the Gopakumar-Vafa Large N Duality
• The Ruled Vertex and Nontoric del Pezzo Surfaces
• Topological Field Theory Amplitudes for $A_{N-1}$ Fibration
• Quantum Barnes function as the partition function of the resolved conifold