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Torus knots and mirror symmetry
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We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants. The curve is obtained by exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we derive the curve as the large N limit of the matrix model computing torus knot invariants.
Forward citations
Cited by 3 Pith papers
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Quantum Curves in the Context of Symplectic Duality
Quantum spectral curve operators for arbitrary base points can be derived by applying x-y and symplectic duality transformations to simpler spectral curves.
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Large-party limit of topological entanglement entropy in Chern-Simons theory
As the number of parties d grows to infinity, the entanglement entropy of Chern-Simons torus-link states is carried only by Abelian anyons and is bounded above by ln|Z_G|.
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Analyzing reduced density matrices in SU(2) Chern-Simons theory
For p-party pure states from T_{p,p} torus link complements in SU(2)_k Chern-Simons theory, the characteristic polynomials of (1|p-1)-reduced density matrices are monic polynomials with rational coefficients.
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