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Abstract |
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. Thus,
this formulation can be also interpreted as a positivity conjecture of refined Chern-Simons
invariants of torus knots/links. |
