Checks of integrality properties in topological strings

Understand

Tests of the integrality properties of a scalar operator in topological strings on a resolved conifold background or orientifold of conifold backgrounds have been performed for arborescent knots and some non-arborescent knots.

• The recent results on polynomials for those knots colored by SU(N) and SO(N) adjoint representations are useful to verify Marino's integrality conjecture up to two boxes in the Young diagram.
• In this paper, we review the salient aspects of the integrality properties and tabulate explicitly for an arborescent knot and a link.
• In our knotebook website, we have put these results for over 100 prime knots available in Rolfsen table and some links.