Closset, CyrilGuo, JiruiSharpe, Eric R.2019-02-272019-02-272018-02-081029-847951http://hdl.handle.net/10919/87865We study 2d 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(infinity) 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 N = (0, 2) gauge theories and certain mutations of exceptional collections of sheaves. 0d N = 1 supersymmetric quivers, corresponding to D-instantons probing CY5 singularities, can be discussed similarly.application/pdfen-USCreative Commons Attribution 4.0 InternationalD-branesField Theories in Lower DimensionsSupersymmetry and DualityTopological StringsB-branes and supersymmetric quivers in 2dArticle - RefereedJournal of High Energy Physicshttps://doi.org/10.1007/JHEP02(2018)0512