BPS states in the Ω-background and torus knots

We clarify some issues concerning the central charges saturated by the extended objects in the SUSY U(1)4d gauge theory in the Ω-background. The configuration involving the monopole localized at the domain wall is considered in some details. At the rational ratio ((ϵ₁)/(ϵ₂))=(p/q) the trajectory of the monopole provides the torus (p,q) knot in the squashed three-sphere. Using the relation between the integrable systems of Calogero type at the rational couplings and the torus knots we interpret this configuration in terms of the auxiliary 2d quiver theory or 3d theory with nontrivial boundary conditions. This realization can be considered as the AGT-like representation of the torus knot invariants