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A supersymmetric quantum mechanical model is constructed for BPS states boundto surface operators in five dimensional SU(r) gauge theories using D-braneengineering. This model represents the effective action of a certain D2-braneconfiguration, and is naturally obtained by dimensional reduction of a quiver$(0,2)$ gauged linear sigma model. In a special stability chamber, theresulting moduli space of quiver representations is shown to be virtuallysmooth and isomorphic to a moduli space of framed quotients on the projectiveplane. A precise conjecture relating a K-theoretic partition function of thismoduli space to refined open string invariants of toric lagrangian branes isformulated for conifold and local P^1 x P^1 geometries.

D-branes, surface operators, and ADHM quiver representations