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Refined large N duality for knots

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  • Masaya Kameyama, Nagoya University, Japan
  • Satoshi Nawata, Fudan Univ, Fudan University, Dept Phys, CALTECH, California Institute of Technology
We formulate large N duality of U(N) refined Chern-Simons theory with a torus
knot/link in S³. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate refined Chern-Simons invariants of a torus knot/link in S³ to refined BPS invariants in the resolved conifold. Assuming that the extra U(1) global symmetry acts on BPS states trivially, the duality predicts graded dimensions of cohomology groups of moduli spaces of M2-M5 bound states associated to a torus knot/link in the resolved conifold.
Original languageEnglish
Number of pages32
Publication statusPublished - Mar 2017

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