# B-branes and supersymmetric quivers in 2d

Journal of High Energy Physics, Feb 2018

Abstract We study 2d $$\mathcal{N}$$ = (0, 2) supersymmetric quiver gauge theories that describe the low-energy dynamics of D1-branes at Calabi-Yau fourfold (CY4) singularities. On general grounds, the holomorphic sector of these theories — matter content and (classical) superpotential interactions — should be fully captured by the topological B-model on the CY4. By studying a number of examples, we confirm this expectation and flesh out the dictionary between B-brane category and supersymmetric quiver: the matter content of the supersymmetric quiver is encoded in morphisms between B-branes (that is, Ext groups of coherent sheaves), while the superpotential interactions are encoded in the A∞ algebra satisfied by the morphisms. This provides us with a derivation of the supersymmetric quiver directly from the CY4 geometry. We also suggest a relation between triality of $$\mathcal{N}$$ = (0,2) gauge theories and certain mutations of exceptional collections of sheaves. 0d $$\mathcal{N}$$ = 1 supersymmetric quivers, corresponding to D-instantons probing CY5 singularities, can be discussed similarly.

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Cyril Closset, Jirui Guo, Eric Sharpe. B-branes and supersymmetric quivers in 2d, Journal of High Energy Physics, 2018, 51, DOI: 10.1007/JHEP02(2018)051