D-branes, surface operators, and ADHM quiver representations

Abstract

A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional $SU(r)$ gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver (0, 2) gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open-string invariants of toric Lagrangian branes is formulated for conifold and local $\mathbb{P}^1 \times \mathbb{P}^1$ geometries.