Colored HOMFLY homology and super-A-polynomial via string theory

I would like to discuss about the knot homology on basis of the string theory. In the categorification of the colored HOMFLY polynomial of knots, we find a triply-graded homology which is named as colored HOMFLY homology.  In the language of string theory, the quantum knot invariants are identified with the generating function of the open Gromov-Witten invariants on conifold with a Lagrangian submanifold associated to the knot diagram. And furthermore, via string dualities, it is conjectured that the colored HOMFLY homology is given by the refined BPS Hilbert space in type IIA superstring theory. From such knot homology, we obtain a knot invariant which is named as colored superpolyonial by taking its Poincare polynomial, and this polynomial refines the colored HOMFLY polynomial and colored Jones polynomial. In this talk, I shall discuss about the analogue of quantum volume conjecture for the colored superpolynomial in completely symmetric representation, and introduce a 2-parameter generalization of A-polynomial which is named as super-A-polynomial.  This talk is based on works in collaboration with H. Awata, S. Gukov, P. Sulkowski, and M. Stosic.