Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torus Knots and the Topological Vertex   We propose a class of toric Lagrangian A-branes on the resolved conifold that
is suitable to describe torus knots on S^3. The key role is played by the
SL(2,Z) transformation, which generates a general torus knot from the unknot.
Applying the topological vertex to the proposed A-branes, we rederive the
colored HOMFLY polynomials for torus knots, in agreement with the Rosso and
Jones formula. We show that our A-model construction is mirror symmetric to the
B-model analysis of Brini, Eynard and Marino. Comparing to the recent proposal
by Aganagic and Vafa for knots on S^3, we demonstrate that the disk amplitude
of the A-brane associated to any knot is sufficient to reconstruct the entire
B-model spectral curve. Finally, the construction of toric Lagrangian A-branes
is generalized to other local toric Calabi-Yau geometries, which paves the road
to study knots in other three-manifolds such as lens spaces.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org