Graded quivers and B-branes at Calabi-Yau singularities

  • Cyril Closset
  • Sebastián FrancoEmail author
  • Jirui Guo
  • Azeem Hasan
Open Access
Regular Article - Theoretical Physics


A graded quiver with superpotential is a quiver whose arrows are assigned degrees c ∈ {0, 1, , m}, for some integer m ≥ 0, with relations generated by a superpotential of degree m − 1. Ordinary quivers (m = 1) often describe the open string sector of D-brane systems; in particular, they capture the physics of D3-branes at local Calabi-Yau (CY) 3-fold singularities in type IIB string theory, in the guise of 4d \( \mathcal{N} \) = 1 supersymmetric quiver gauge theories. It was pointed out recently that graded quivers with m = 2 and m=3 similarly describe systems of D-branes at CY 4-fold and 5-fold singularities, as 2d \( \mathcal{N} \) = (0, 2) and 0d \( \mathcal{N} \) = 1 gauge theories, respectively. In this work, we further explore the correspondence between m-graded quivers with superpotential, Q(m), and CY (m + 2)-fold singularities, Xm+2. For any m, the open string sector of the topological B-model on Xm+2 can be described in terms of a graded quiver. We illustrate this correspondence explicitly with a few infinite families of toric singularities indexed by m ∈ ℕ, for which we derive “toric” graded quivers associated to the geometry, using several complementary perspectives. Many interesting aspects of supersymmetric quiver gauge theories can be formally extended to any m; for instance, for one family of singularities, dubbed C(Y1,0(ℙm)), that generalizes the conifold singularity to m > 1, we point out the existence of a formal “duality cascade” for the corresponding graded quivers.


D-branes Supersymmetry and Duality Topological Strings 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Cyril Closset
    • 1
  • Sebastián Franco
    • 2
    • 3
    Email author
  • Jirui Guo
    • 4
  • Azeem Hasan
    • 2
    • 3
  1. 1.Mathematical InstituteUniversity of OxfordOxfordU.K.
  2. 2.Physics DepartmentThe City College of the CUNYNew YorkU.S.A.
  3. 3.The Graduate School and University CenterThe City University of New YorkNew YorkU.S.A.
  4. 4.Department of Physics and Center for Field Theory and Particle PhysicsFudan UniversityShanghaiChina

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