B-branes and supersymmetric quivers in 2d

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 (CY${}_4$) 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 CY${}_4$. 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 $A_{\infty }$ algebra satisfied by the morphisms. This provides us with a derivation of the supersymmetric quiver directly from the CY${}_4$ 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 CY${}_5$ singularities, can be discussed similarly.

63 pages plus appendix, 21 figures; v2: corrected typos and added reference. JHEP version; v3: added reference

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Cited by in corpus (14)

• $3d$ Printing of $2d$ $\mathcal{N}=(0,2)$ Gauge Theories
• Holomorphic field theories and Calabi--Yau algebras
• The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0,2) F-theory Vacua
• Fano 3-Folds, Reflexive Polytopes and Brane Brick Models
• Graded Quivers, Generalized Dimer Models and Toric Geometry
• The Origin of Calabi-Yau Crystals in BPS States Counting
• Charging solid partitions
• Supersymmetric gauged matrix models from dimensional reduction on a sphere
• Remarks on 2d Unframed Quiver Gauge Theories
• On the Classification of Duality Webs for Graded Quivers
• Some Open Questions in Quiver Gauge Theory
• Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials
• Elliptic Calabi-Yau fivefolds and 2d (0,2) F-theory landscape
• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials