TY - JOUR

T1 - Graded quivers and B-branes at Calabi-Yau singularities

AU - Closset, C.

AU - Franco, S.

AU - Guo, J.

AU - Hasan, A.

PY - 2019/3/11

Y1 - 2019/3/11

N2 - 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 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 N = (0, 2) and 0d 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.

AB - 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 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 N = (0, 2) and 0d 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.

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85063054868&partnerID=MN8TOARS

U2 - 10.1007/JHEP03(2019)053

DO - 10.1007/JHEP03(2019)053

M3 - Article

SN - 1126-6708

JO - JHEP

JF - JHEP

M1 - 53

ER -