2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189584We study the relation between two kinds of topological amplitudes of non-compact D-branes on conifold. In the A-model, D-branes are represented by fermion operators in the melting crystal picture and the amplitudes are given by the quantum dilogarithm. In the mirror B-model, D-branes correspond to the determinant operator det(x-M) in the Chern-Simons matrix model and the amplitudes are given by the Stieltjes-Wigert polynomial. We show that these two amplitudes are related by a certain integral transformation. We argue that this transformation represents the deformation of closed string background due to the presence of D-branes.13 pages; v2:references addedHigh Energy Physics - Theorytext