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D-branes, surface operators, and ADHM quiver representations. (English) Zbl 1261.81089

The main goal of this paper is to construct a microscopic quantum-mechanical model for Bogomolny, Prasad, Sommerfeld (BPS) states bound to certain surface operators in minimally supersymmetric \(\mathrm{SU}(r)\) gauge theories. This model is obtained employing a string theory construction of such theories consisting of IIA D-branes in a nontrivial geometric background. The BPS states are engineered in terms of D2-brane configurations, the resulting low-energy effective action being naturally constructed as the dimensional reduction of a \((0, 2)\) quiver 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.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
83E15 Kaluza-Klein and other higher-dimensional theories
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