  We demonstrate explicitly that the vacuum expectation values (vevs) of BPS
line operators in 4d N=2 super Yang-Mills theory compactified on a circle,
computed by localization techniques, can be expanded in terms of Darboux
coordinates as proposed by Gaiotto, Moore, and Neitzke [arXiv:1006.0146].
However, we need to refine the expansion by including additional novel monopole
bubbling contributions to obtain a precise match. Using D-brane realization of
these singular BPS line operators, we derive and incorporate the monopole
bubbling contributions as well as predict the degeneracies of framed BPS states
contributing to the line operator vevs in the limit of vanishing simultaneous
spatial and R-symmetry rotation fugacity parameter.
