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Journal of High Energy Physics

, 2018:51 | Cite as

B-branes and supersymmetric quivers in 2d

  • Cyril Closset
  • Jirui Guo
  • Eric Sharpe
Open Access
Regular Article - Experimental Physics

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.

Keywords

D-branes Field Theories in Lower Dimensions Supersymmetry and Duality Topological Strings 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Theory DepartmentCERNGeneva 23Switzerland
  2. 2.Department of PhysicsFudan UniversityShanghaiChina
  3. 3.Department of Physics MC 0435BlacksburgU.S.A.

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