Refined Chern-Simons Theory and Topological String
Mina Aganagic, Shamil Shakirov

TL;DR
This paper connects refined Chern-Simons theory with topological string theory, deriving the refined topological vertex from link invariants, and explores dualities and mirror symmetry in refined invariants for toric Calabi-Yau manifolds.
Contribution
It derives the refined topological vertex from refined Chern-Simons theory and proposes a formalism for arbitrary toric Calabi-Yau manifolds using a pair of vertices and Morse flow.
Findings
Derived the refined topological vertex from link invariants.
Established dual descriptions of toric Calabi-Yau manifolds with branes.
Linked large N duality to mirror symmetry of refined knot invariants.
Abstract
We show that refined Chern-Simons theory and large N duality can be used to study the refined topological string with and without branes. We derive the refined topological vertex of hep-th/0701156 and hep-th/0502061 from a link invariant of the refined SU(N) Chern-Simons theory on S^3, at infinite N. Quiver-like Chern-Simons theories, arising from Calabi-Yau manifolds with branes wrapped on several minimal S^3's, give a dual description of a large class of toric Calabi-Yau. We use this to derive the refined topological string amplitudes on a toric Calabi-Yau containing a shrinking P^2 surface. The result is suggestive of the refined topological vertex formalism for arbitrary toric Calabi-Yau manifolds in terms of a pair of vertices and a choice of a Morse flow on the toric graph, determining the vertex decomposition. The dependence on the flow is reminiscent of the approach to the…
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Topological and Geometric Data Analysis · Noncommutative and Quantum Gravity Theories
